EnVision Algebra 2 Alabama 2022 - Alabama Course of Study Mathematics 2019 Algebra II with Statistics - A Correlation of - Savvas Learning ...

A Correlation of

enVision Algebra 2 Alabama
 ©2022

 To the

 Alabama Course of Study
 Mathematics 2019
 Algebra II with Statistics

A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

Student Mathematical Practices
1. Make sense of problems and persevere in SE/TE: 47-54, 73-79, 88-94, 162-169, 193-200,
solving them. 224-231, 239-246, 263-271, 273-280, 305-312,
 333-339, 365-375, 393-399, 489-497, 551-557,
 558-564, 589-596, 613-620, 643-649

2. Reason abstractly and quantitatively. SE/TE: 47-54, 131-138, 139-145, 146-153, 154-
 161, 171-178, 201-209, 224-231, 247-254, 255-
 262, 281-289, 297-304, 314-320, 327-332, 333-
 339, 340-348, 357-364, 365-375, 376-382, 424-
 432, 433-440, 463-471, 472-478, 480-488, 511-
 517, 518-527, 528-536, 564-572, 605-612, 613-
 620, 628-635, 636-642, 643-649

3. Construct viable arguments and critique the SE/TE: 5-12, 23-30, 31-39, 40-46, 56-64, 73-79,
reasoning of others. 80-87, 88-94, 103-109, 110-116, 117-123, 139-
 145, 146-153, 179-186, 193-200, 210-216, 263-
 271, 321-326, 376-382, 383-391, 400-407, 415-
 422, 433-440, 441-448, 449-456, 511-517, 558-
 564, 573-580, 589-596, 605-612, 613-620, 621-
 627, 636-642

4. Model with mathematics. SE/TE: 5-12, 13-22, 31-39, 55, 80-87, 95-101,
 102, 117-123, 170, 239-246, 247-254, 255-262,
 272, 297-304, 305-312, 313, 314-320, 321-326,
 327-392, 332, 376-382, 383-391, 423, 472-478,
 479, 480-488, 489-497, 503-510, 544, 597, 620,
 621-627, 628-635, 636-642, AL-11-4b

5. Use appropriate tools strategically. SE/TE: 13-22, 40-46, 56-64, 110-116, 131-138,
 171-178, 217-223, 239-246, 340-348, 365-375,
 415-422, 424-432, 449-456, 528-536, 564-572,
 573-580, 581-588, AL-8-2a, AL-10-2a, AL-11-4b,
 AL-11-5a

6. Attend to precision. SE/TE: 23-30, 103-109, 154-161, 201-209, 210-
 216, 273-280, 281-289, 503-510, 537-543, 551-
 557, 564-572, 581-588, 589-596, 628-635, AL-8-
 2a

 1
 SE = Student Edition TE = Teacher’s Edition

A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

7. Look for and make use of structure. SE/TE: 5-12, 13-22, 23-30, 31-39, 40-46, 47-54,
 56-64, 73-79, 80-87, 88-94, 95-101, 103-109,
 110-116, 117-123, 131-138, 139-145, 146-153,
 154-161, 162-169, 171-178, 179-186, 201-209,
 210-216, 217-223, 224-231, 247-254, 255-262,
 263-271, 273-280, 281-289, 297-304, 305-312,
 314-320, 321-326, 327-332, 333-339, 340-348,
 357-364, 383-391, 393-399, 400-407, 415-422,
 424-432, 433-440, 441-448, 449-456, 463-471,
 472-478, 489-497, 503-510, 511-517, 518-527,
 528-536, 537-543, 558-564, 573-580, 605-612,
 613-620, 621-627, AL-10-2a, AL-11-5a

8. Look for and express regularity in repeated SE/TE: 95-101, 162-169, 357-364, 393-399, 400-
reasoning. 407, 441-448, 463-471, 518-527, 537-543, 551-
 557, AL-11-4a

Algebra II with Statistics Content Standards
Number and Quantity
Together, irrational numbers and rational numbers complete the real number system, representing all
points on the number line, while there exist numbers beyond the real numbers called complex
numbers.
1. Identify numbers written in the form a + bi, SE: 95-101
where a and b are real numbers and i2 = –1, as
complex numbers. TE: 95A-101B

a. Add, subtract, and multiply complex numbers SE: 95-101
using the commutative, associative, and
distributive properties. TE: 95A-101B

Matrices are a useful way to represent information.
2. Use matrices to represent and manipulate data. SE: 503-510, 544

 TE: 503A-510B, 544-544B

3. Multiply matrices by scalars to produce new SE: 503-510
matrices.
 TE: 503A-510B

4. Add, subtract, and multiply matrices of SE: 503-510, 511-517
appropriate dimensions.
 TE: 503A-510B, 511A-517B

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A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

5. Describe the roles that zero and identity SE: 503-510, 511-517, 528-536
matrices play in matrix addition and multiplication,
recognizing that they are similar to the roles of 0 TE: 503A-510B, 511A-517B, 528A-536B
and 1 in the real numbers.

a. Find the additive and multiplicative inverses of SE: 528-536
square matrices, using technology as appropriate.
 TE: 528A-536B

b. Explain the role of the determinant in SE: AL10-2A, 528-536
determining if a square matrix has a multiplicative
inverse. TE: AL10-2A, 528A-536B

Algebra and Functions
Focus 1: Algebra
Expressions can be rewritten in equivalent forms by using algebraic properties, including properties of
addition, multiplication, and exponentiation, to make different characteristics or features visible.
6. Factor polynomials using common factoring SE: 88-94, 146-153, 162-169, 170
techniques, and use the factored form of a
polynomial to reveal the zeros of the function it TE: 88A-94B, 146A-153B, 162A-169B, 170-170B
defines.

7. Prove polynomial identities and use them to SE: 146-153, 170
describe numerical relationships.
Example: The polynomial identity 1 – xn = (1 – x)(1 TE: 146A-153B, 170-170B
+ x + x 2 + x3 + … + xn-1 + xn) can be used to find
the sum of the first n terms of a geometric
sequence with common ratio x by dividing both
sides of the identity by (1 - x).

Finding solutions to an equation, inequality, or system of equations or inequalities requires the
checking of candidate solutions, whether generated analytically or graphically, to ensure that solutions
are found and that those found are not extraneous.
8. Explain why extraneous solutions to an SE: 224-231, 263-271
equation may arise and how to check to be sure
that a candidate solution satisfies an equation. TE: 224A-236B, 263A-271B
Extend to radical equations.

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A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

The structure of an equation or inequality (including, but not limited to, one-variable linear and
quadratic equations, inequalities, and systems of linear equations in two variables) can be purposefully
analyzed (with and without technology) to determine an efficient strategy to find a solution, if one exists,
and then to justify the solution.
9. For exponential models, express as a logarithm SE: 314-320, 327-332, 333-339
the solution to abct = d, where a, c, and d are real
numbers and the base b is 2 or 10; evaluate the TE: 314A-320B, 327A-332B, 333A-339B
logarithm using technology to solve an
exponential equation.

Expressions, equations, and inequalities can be used to analyze and make predictions, both within
mathematics and as mathematics is applied in different contexts—in particular, contexts that arise in
relation to linear, quadratic, and exponential situations.
10. Create equations and inequalities in one SE: 40-46, 263-271, 333-339, 415-422
variable and use them to solve problems. Extend
to equations arising from polynomial, TE: 40A-46B, 263A-271B, 333A-339B, 415A-
trigonometric (sine and cosine), logarithmic, 422B
radical, and general piecewise functions.

11. Solve quadratic equations with real SE: 103-109, 110-116, 272
coefficients that have complex solutions.
 TE: 103A-109B, 110A-116B, 272-272B

12. Solve simple equations involving exponential, SE: 263-271, 314-320, 333-339, 415-420
radical, logarithmic, and trigonometric functions
using inverse functions. TE: 263A-27AB, 314A-320B, 333A-339B, 415A-
 420B

13. Create equations in two or more variables to SE: 23-30, 131-138, 162-169, 193-200, 201-209,
represent relationships between quantities; graph 255-262, 297-304, 305-312, 321-326, 383-391
equations on coordinate axes with labels and
scales and use them to make predictions. Extend TE: 23A-30B, 131A-138B, 162A-169B, 193A-
to polynomial, trigonometric (sine and cosine), 200B, 201A-209B, 255A-262B, 297A-304B, 305A-
logarithmic, reciprocal, radical, and general 312B, 321A-326B, 383A-391B
piecewise functions.

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A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

Focus 2: Connecting Algebra to Functions
Graphs can be used to obtain exact or approximate solutions of equations, inequalities, and systems of
equations and inequalities—including systems of linear equations in two variables and systems of
linear and quadratic equations (given or obtained by using technology).
14. Explain why the x-coordinates of the points SE: 40-46, 224-231, 263-271, 333-339, 415-422
where the graphs of the equations y = f(x) and y =
g(x) intersect are the solutions of the equation f(x) TE: 40A-46B, 224A-231B, 263A-271B, 333A-
= g(x). 339B, 415A-422B

a. Find the approximate solutions of an equation SE: 40-46, 224-231, 263-271, 333-339, 415-422
graphically, using tables of values, or finding
successive approximations, using technology TE: 40A-46B, 224A-231B, 263A-271B, 333A-
where appropriate. Extend to cases where f(x) 339B, 415A-422B
and/or g(x) are polynomial, trigonometric (sine
and cosine), logarithmic, radical, and general
piecewise functions.

Focus 3: Functions
Functions can be described by using a variety of representations: mapping diagrams, function notation
(e.g., f(x) = x2), recursive definitions, tables, and graphs.
15. Compare properties of two functions each SE: 23-30, 139-145, 255-262, 297-304, 321-326,
represented in a different way (algebraically, 383-391
graphically, numerically in tables, or by verbal
descriptions). Extend to polynomial, TE: 23A-30B, 139A-145B, 255A-262B, 297A-
trigonometric (sine and cosine), logarithmic, 304B, 321A-326B, 383A-391B
radical, and general piecewise functions.

Functions that are members of the same family have distinguishing attributes (structure) common to all
functions within that family.
16. Identify the effect on the graph of replacing SE: 13-22, 73-79, 179-186, 193-200, 255-262,
 ( ) by ( )+ , ꞏ ( ), ( ꞏ ), and ( + ) for 297-304, 321-326, 383-391, 393-399, 400-407
specific values of k (both positive and negative);
find the value of k given the graphs. Experiment TE: 23A-30B, 139A-145B, 255A-262B, 297A-
with cases and illustrate an explanation of the 304B, 321A-326B, 383A-391B, 393A-399B, 400A-
effects on the graph using technology. Extend to 407B
polynomial, trigonometric (sine and cosine),
logarithmic, reciprocal, radical, and general
piecewise functions.

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 SE = Student Edition TE = Teacher’s Edition

A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

Functions can be represented graphically, and key features of the graphs, including zeros, intercepts,
and, when relevant, rate of change and maximum/minimum values, can be associated with and
interpreted in terms of the equivalent symbolic representation.
17. For a function that models a relationship SE: 5-12, 23-30, 73-79, 80-87, 102, 131-138, 170,
between two quantities, interpret key features of 193-200, 201-209, 255-262, 297-304, 321-326,
graphs and tables in terms of the quantities, and 393-399, 400-407
sketch graphs showing key features given a
verbal description of the relationship. Note: Key TE: 5A-12B, 23A-30B, 73A-79B, 80A-87B, 102-
features include intercepts; intervals where the 102B, 131A-138B, 170-170B, 193A-200B, 201A-
function is increasing, decreasing, positive, or 209B, 255A-262B, 297A-304B, 321A-326B, 393A-
negative; maximums and minimums; symmetries 399B, 400A-407B
(including even and odd); end behavior; and
periodicity. Extend to polynomial, trigonometric
(sine and cosine), logarithmic, reciprocal,
radical, and general piecewise functions.

18. Relate the domain of a function to its graph SE: 23-30, 73-79, 131-138,193-200, 201-209,
and, where applicable, to the quantitative 255-262, 297-304, 321-326, 383-391, 393-399
relationship it describes. Extend to polynomial,
trigonometric (sine and cosine), logarithmic, TE: 23A-30B, 73A-79B, 131A-138B,193A-200B,
reciprocal, radical, and general piecewise 201A-209B, 255A-262B, 297A-304B, 321A-326B,
functions. 383A-391B, 393A-399B

19. Calculate and interpret the average rate of SE: 5-12, 23-30,131-138, 255-262, 297-304, 321-
change of a function (presented symbolically or as 326, 383-391
a table) over a specified interval. Estimate the rate
of change from a graph. Extend to polynomial, TE: 5A-12B, 23A-30B,131A-138B, 255A-262B,
trigonometric (sine and cosine), logarithmic, 297A-304B, 321A-326B, 383A-391B
reciprocal, radical, and general piecewise
functions.

20. Graph functions expressed symbolically and SE: 131-138, 162-169, 171-178, 193-200, 201-
show key features of the graph, by hand in simple 209, 255-262, 281-289, 321-326, 383-391, 400-
cases and using technology for more complicated 407
cases. Extend to polynomial, trigonometric
(sine and cosine), logarithmic, reciprocal, TE: 131A-138B, 162A-169B, 171A-178B, 193A-
radical, and general piecewise functions. 200B, 201A-209B, 255A-262B, 281A-289B, 321A-
 326B, 383A-391B, 400A-407B

a. Graph polynomial functions expressed SE: 131-138, 162-169, 171-178
symbolically, identifying zeros when suitable
factorizations are available, and showing end TE: 131A-138B, 162A-169B, 171A-178B
behavior.

b. Graph sine and cosine functions expressed SE: 383-391, 392, 400-407
symbolically, showing period, midline, and
amplitude. TE: 383A-391B, 392-392B, 400A-407B

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A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

c. Graph logarithmic functions expressed SE: 321-326
symbolically, showing intercepts and end
behavior. TE: 321A-326B

d. Graph reciprocal functions expressed SE: 193-200, 201-209
symbolically, identifying horizontal and vertical
asymptotes. TE: 193A-200B, 201A-209B

e. Graph square root and cube root functions SE: 255-262
expressed symbolically.
 TE: 255A-262B

f. Compare the graphs of inverse functions and SE: 281-289, 321-326
the relationships between their key features,
including but not limited to quadratic, square root, TE: 281A-289B, 321A-326B
exponential, and logarithmic functions.

21. Explain how the unit circle in the coordinate SE: 365-375, 376-382
plane enables the extension of trigonometric
functions to all real numbers, interpreted as radian TE: 365A-375B, 376A-382B
measures of angles traversed counterclockwise
around the unit circle, building on work with non-
right triangle trigonometry.

Functions model a wide variety of real situations and can help students understand the processes of
making and changing assumptions, assigning variables, and finding solutions to contextual problems.
22. Use the mathematical modeling cycle to solve SE: 102, 170, 272, 313, 392, 423
real world problems involving polynomial,
trigonometric (sine and cosine), logarithmic, TE: 102-102B, 170-170B, 272-272B, 313-313B,
radical, and general piecewise functions, from the 392-392B, 423-423B
simplification of the problem through the solving of
the simplified problem, the interpretation of its
solution, and the checking of the solution’s
feasibility.

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A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

Data Analysis, Statistics, and Probability
Focus 1: Quantitative Literacy
Mathematical and statistical reasoning about data can be used to evaluate conclusions and assess
risks.
23. Use mathematical and statistical reasoning SE: 581-588
about normal distributions to draw conclusions
and assess risk; limit to informal arguments. TE: 581A-588B
Example: If candidate A is leading candidate B by
2% in a poll which has a margin of error of less
than 3%, should we be surprised if candidate B
wins the election?

Making and defending informed data-based decisions is a characteristic of a quantitatively literate
person.
24. Design and carry out an experiment or survey SE: 551-557, 558-564, 565-572, 573-580, 581-
to answer a question of interest, and write an 588, 589-596
informal persuasive argument based on the
results. TE: 551A-557B, 558A-564B, 565A-572B, 573A-
Example: Use the statistical problem-solving cycle 580B, 581A-588B, 589A-596B
to answer the question, “Is there an association
between playing a musical instrument and doing
well in mathematics?”

Focus 2: Visualizing and Summarizing Data
Distributions of quantitative data (continuous or discrete) in one variable should be described in the
context of the data with respect to what is typical (the shape, with appropriate measures of center and
variability, including standard deviation) and what is not (outliers), and these characteristics can be
used to compare two or more subgroups with respect to a variable.
25. From a normal distribution, use technology to SE: 565-572, 573-580
find the mean and standard deviation and
estimate population percentages by applying the TE: 565A-572B, 573A-580B
empirical rule.

a. Use technology to determine if a given set of SE: AL11-4b
data is normal by applying the empirical rule.
 TE: AL11-4b

b. Estimate areas under a normal curve to solve SE: 573-580
problems in context, using calculators,
spreadsheets, and tables as appropriate. TE: 573A-580B

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A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

Focus 3: Statistical Inference
Study designs are of three main types: sample survey, experiment, and observational study.
26. Describe the purposes of and differences SE: 558-564
among sample surveys, experiments, and
observational studies; explain how randomization TE: 558A-564B
relates to each.
Examples: random assignment in experiments,
random selection in surveys and observational
studies

The role of randomization is different in randomly selecting samples and in randomly assigning
subjects to experimental treatment groups.
27. Distinguish between a statistic and a SE: 551-557, 558-564, 581-588, 589-596, 597
parameter and use statistical processes to make
inferences about population parameters based on TE: 551A-557B, 558A-564B, 581A-588B, 589A-
statistics from random samples from that 596B, 597-597B
population.

28. Describe differences between randomly SE: 558-564
selecting samples and randomly assigning
subjects to experimental treatment groups in TE: 558A-564B
terms of inferences drawn regarding a population
versus regarding cause and effect.
Example: Data from a group of plants randomly
selected from a field allows inference regarding
the rest of the plants in the field, while randomly
assigning each plant to one of two treatments
allows inference regarding differences in the
effects of the two treatments. If the plants were
both randomly selected and randomly assigned,
we can infer that the difference in effects of the
two treatments would also be observed when
applied to the rest of the plants in the field.

The scope and validity of statistical inferences are dependent on the role of randomization in the study
design.
29. Explain the consequences, due to SE: 558-564, 597
uncontrolled variables, of non-randomized
assignment of subjects to groups in experiments. TE: 558A-564B, 597-597B
Example: Students are studying whether or not
listening to music while completing mathematics
homework improves their quiz scores. Rather than
assigning students to either listen to music or not
at random, they simply observe what the students
do on their own and find that the music-listening
group has a higher mean quiz score. Can they
conclude that listening to music while studying is
likely to raise the quiz scores of students who do
not already listen to music? What other factors
may have been responsible for the observed
difference in mean quiz scores?

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A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

Bias, such as sampling, response, or nonresponse bias, may occur in surveys, yielding results that are
not representative of the population of interest.
30. Evaluate where bias, including sampling, SE: 558-564
response, or nonresponse bias, may occur in
surveys, and whether results are representative of TE: 558A-564B
the population of interest.
Example: Selecting students eating lunch in the
cafeteria to participate in a survey may not
accurately represent the student body, as
students who do not eat in the cafeteria may not
be accounted for and may have different opinions,
or students may not respond honestly to
questions that may be embarrassing, such as how
much time they spend on homework.

The larger the sample size, the less the expected variability in the sampling distribution of a sample
statistic.
31. Evaluate the effect of sample size on the SE: AL11-4a
expected variability in the sampling distribution of
a sample statistic. TE: AL11-4a

a. Simulate a sampling distribution of sample SE: AL11-4a
means from a population with a known
distribution, observing the effect of the sample TE: AL11-4a
size on the variability.

b. Demonstrate that the standard deviation of SE: AL11-4a
each simulated sampling distribution is the known
standard deviation of the population divided by the TE: AL11-4a
square root of the sample size.

The sampling distribution of a sample statistic formed from repeated samples for a given sample size
drawn from a population can be used to identify typical behavior for that statistic. Examining several
such sampling distributions leads to estimating a set of plausible values for the population parameter,
using the margin of error as a measure that describes the sampling variability.
32. Produce a sampling distribution by repeatedly SE: AL11-5a
selecting samples of the same size from a given
population or from a population simulated by TE: AL11-5a
bootstrapping (resampling with replacement from
an observed sample). Do initial examples by
hand, then use technology to generate a large
number of samples.

a. Verify that a sampling distribution is centered at SE: AL11-4a
the population mean and approximately normal if
the sample size is large enough. TE: AL11-4a

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A Correlation of enVision Algebra 2 Alabama, ©2022
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 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

b. Verify that 95% of sample means are within two SE: AL11-5a
standard deviations of the sampling distribution
from the population mean. TE: AL11-5a

c. Create and interpret a 95% confidence interval SE: AL11-5a
based on an observed mean from a sampling
distribution. TE: AL11-5a

33. Use data from a randomized experiment to SE: 589-596
compare two treatments; limit to informal use of
simulations to decide if an observed difference in TE: 589A-596B
the responses of the two treatment groups is
unlikely to have occurred due to randomization
alone, thus implying that the difference between
the treatment groups is meaningful.
Example: Fifteen students are randomly assigned
to a treatment group that listens to music while
completing mathematics homework and another
15 are assigned to a control group that does not,
and their means on the next quiz are found to be
different. To test whether the differences seem
significant, all the scores from the two groups are
placed on index cards and repeatedly shuffled into
two new groups of 15 each, each time recording
the difference in the means of the two groups. The
differences in means of the treatment and control
groups are then compared to the differences in
means of the mixed groups to see how likely it is
to occur.

Geometry and Measurement
Focus 1: Measurement
When an object is the image of a known object under a similarity transformation, a length, area, or
volume on the image can be computed by using proportional relationships.
34. Define the radian measure of an angle as the SE: 365-375
constant of proportionality of the length of an arc it
intercepts to the radius of the circle; in particular, it TE: 365A-375B
is the length of the arc intercepted on the unit
circle.

Focus 2: Transformations (Note: There are no Algebra II with Statistics standards in Focus 2)
Focus 3: Geometric Argument, Reasoning, and Proof (Note: There are no Algebra II with Statistics
standards in Focus 3)
Focus 4: Solving Applied Problems and Modeling in Geometry
Recognizing congruence, similarity, symmetry, measurement opportunities, and other geometric ideas,
including right triangle trigonometry in real-world contexts, provides a means of building understanding
of these concepts and is a powerful tool for solving problems related to the physical world in which we
live.

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A Correlation of enVision Algebra 2 Alabama, ©2022
 To the Alabama Course of Study Mathematics 2019 Algebra II with Statistics

 Alabama Course of Study Mathematics 2019 enVision Algebra 2 Alabama
 Algebra II with Statistics ©2022

 35. Choose trigonometric functions (sine and SE: 383-391, 400-407
 cosine) to model periodic phenomena with
 specified amplitude, frequency, and midline. TE: 383A-391B, 400A-407B

 36. Prove the Pythagorean identity sin2 (θ) + cos2 SE: 376-382
 (θ) = 1 and use it to calculate trigonometric ratios.
 TE: 376A-382B

 37. Derive and apply the formula A = ½ꞏabꞏsin(C) SE: AL8-2a
 for the area of a triangle by drawing an auxiliary
 line from a vertex perpendicular to the opposite TE: AL8-2a
 side, extending the domain of sine to include right
 and obtuse angles.

 38. Derive and apply the Law of Sines and the SE: 424-432
 Law of Cosines to find unknown measurements in
 right and non-right triangles. Extend the domain of TE: 424A-432B
 sine and cosine to include right and obtuse
 angles.
 Examples: surveying problems, resultant forces

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