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Franklin HS Algebra 2 Topic 7 Review - Printable Mathematics Worksheets year 12 - Wayground

Franklin HS Algebra 2 Topic 7 Review

17 questions

9th - 12th Grade

Mathematics

Franklin HS Algebra 2 Topic 7 Review is a free printable worksheet with an answer key for Grades 9–12 mathematics. It provides 17 review items in multiple-choice, multiple-select, drawing, fill-in-the-blank, and open-ended formats, giving students varied practice with trigonometric ratios, quadrant-based angle reasoning, reference angles, radian measures, and right-triangle applications. The worksheet also focuses on interpreting and graphing sinusoidal functions. Students identify amplitude, period, frequency, and midline; determine sine and cosine values; recognize graph representations; sketch a function; and describe transformations. Its combination of selected-response questions and constructed responses helps teachers check both procedural fluency and whether students can explain or represent trigonometric ideas independently.

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Worksheets

Franklin HS Algebra 2 Topic 7 Review

Total questions: 17

Name
Class
Date
1.

In the equation, y=3sin⁡(14)x, y=3\sin\left(\frac{1}{4}\right)x,\ identify the

period: ___________

a)

8π8\pi

b)

4π4\pi

c)

2π2\pi

d)

π\pi

2.

In the equation y=12cos⁡(12)x,y=\frac{1}{2}\cos\left(\frac{1}{2}\right)x, what is the amplitude?

a)

12\frac{1}{2}

b)

2

c)

14\frac{1}{4}

d)

π2\frac{\pi}{2}

3.

Given that tan⁡x=247\tan x=\frac{24}{7} and is found in Quadrant I, which of the following trig ratios are correct?.​

a)

sin⁡x=2425\sin x=\frac{24}{25}

b)

cos⁡x=725\cos x=\frac{7}{25}

c)

sec⁡x=2524\sec x=\frac{25}{24}

d)

csc⁡x=257\csc x=\frac{25}{7}

e)

cot⁡x=2524\cot x=\frac{25}{24}

4.

Given that sin⁡θ=0.5667\sin\theta=0.5667 and π2<θ<π,\frac{\pi}{2}<\theta<\pi, using sin⁡2θ+cos⁡2θ=1\sin^2\theta+\cos^2\theta=1 , what is the approximate value of cos⁡θ?\cos\theta? Round your answer to the nearest ten thousandths.

a)

1.14941.1494

b)

1.25171.2517

c)

0.65830.6583

d)

−0.8339-0.8339

5.

What are the sine and cosine of π6\frac{\pi}{6} ?

a)

sin⁡θ=32and cos⁡θ=12\sin\theta=\frac{\sqrt[]{3}}{2}and\ \cos\theta=\frac{1}{2}

b)

sin⁡θ=12and cos⁡θ=32\sin\theta=\frac{1}{2}and\ \cos\theta=\frac{\sqrt[]{3}}{2}

c)

sin⁡θ=233and cos⁡θ=12\sin\theta=\frac{2\sqrt[]{3}}{3}and\ \cos\theta=\frac{1}{2}

d)

sin⁡θ=12and cos⁡θ=233\sin\theta=\frac{1}{2}and\ \cos\theta=\frac{2\sqrt[]{3}}{3}

6.

An angle has a reference angle measuring 50°50\degree and its terminal side lies in Quadrant III. What are the positive and negative measures for the angle?

a)

230° and −40°230\degree\ and\ -40\degree

b)

220° and −140°220\degree\ and\ -140\degree

c)

230° and −130°230\degree\ and\ -130\degree

d)

220° and −50°220\degree\ and\ -50\degree

7.

Which of the following is the graph of the function f(x)=12cos⁡(x)−1f\left(x\right)=\frac{1}{2}\cos\left(x\right)-1 ?

a)

b)

c)

d)

8.

What is cos⁡θ\cos\theta if sin⁡θ=45\sin\theta=\frac{4}{5} and θ\theta is in Quadrant III?

a)

cos⁡θ=34\cos\theta=\frac{3}{4}

b)

cos⁡θ=45\cos\theta=\frac{4}{5}

c)

cos⁡θ=35\cos\theta=\frac{3}{5}

d)

cos⁡θ=−35\cos\theta=-\frac{3}{5}

9.

Which of the following are measures of the angle shown?

a)

−560°-560\degree

b)

560°560\degree

c)

−520°-520\degree

d)

520°520\degree

e)

−200°-200\degree

10.

A 20-foot ladder leans against the side of a tree at a 48°48\degree angle with the ground. Find the distance from the base of the ladder to the house.

a)

13.38 ft13.38\ ft

b)

12.8 ft12.8\ ft

c)

31.24 ft31.24\ ft

d)

29.89 ft29.89\ ft

11.

Find the radian measure of 405°.405\degree. Give the exact simplified answer in terms of π\pi .

a)

5π9\frac{5\pi}{9}

b)

9π5\frac{9\pi}{5}

c)

4π9\frac{4\pi}{9}

d)

9π4\frac{9\pi}{4}

12.

Sketch the graph of f(x)=−2cos⁡(4x)f\left(x\right)=-2\cos\left(4x\right) .

13.

What is the frequency of the graph of y=3cos⁡(2x)?y=3\cos\left(2x\right)?

(a)  

14.

Describe the transformation of the graph of g(x)=2cos⁡(x−π4)g\left(x\right)=2\cos\left(x-\frac{\pi}{4}\right) from the graph of f(x)=cos⁡x.f\left(x\right)=\cos x.

4 lines
15.

What is the equation of the midline of the graph of y=4cos⁡(x2)+2?y=4\cos\left(\frac{x}{2}\right)+2?

(a)  

16.

Find all the five trig ratios given that cos⁡θ=1517\cos\theta=\frac{15}{17} and is found in Quadrant I.

17.

Given that cos⁡θ=0.67,\cos\theta=0.67, using sin⁡2θ+cos⁡2θ=1,\sin^2\theta+\cos^2\theta=1, find sin⁡θ\sin\theta (in Quadrant I). Show all your work fo credit. Round your answer to three decimal approximation.

4 lines
Answer Key

Franklin HS Algebra 2 Topic 7 Review

Total questions: 17

1.
a)

8π8\pi

2.
a)

12\frac{1}{2}

3.
a)

sin⁡x=2425\sin x=\frac{24}{25}

, b)

cos⁡x=725\cos x=\frac{7}{25}

4.
d)

−0.8339-0.8339

5.
b)

sin⁡θ=12and cos⁡θ=32\sin\theta=\frac{1}{2}and\ \cos\theta=\frac{\sqrt[]{3}}{2}

6.
c)

230° and −130°230\degree\ and\ -130\degree

7.
a)

8.
d)

cos⁡θ=−35\cos\theta=-\frac{3}{5}

9.
b)

560°560\degree

, c)

−520°-520\degree

10.
a)

13.38 ft13.38\ ft

11.
d)

9π4\frac{9\pi}{4}

12.
n/a
13.
2
14.
n/a
15.
y=2
16.
n/a
17.
n/a

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FAQs

What does the Franklin HS Algebra 2 Topic 7 Review worksheet cover?

This worksheet reviews trigonometric ratios and angle measures alongside sinusoidal-function features such as amplitude, period, frequency, midline, graph transformations, and equations. Its 17 items use multiple choice, multiple select, drawing, fill-in-the-blank, and open-ended formats, requiring students to calculate values, interpret quadrants and reference angles, sketch graphs, and explain transformations.

How can I use this worksheet to teach trigonometric ratios and sinusoidal graphs?

Use the selected-response items to introduce or review quadrant signs, reference angles, radian measures, and right-triangle applications before moving to the graphing tasks. Then have students sketch a sinusoidal function and explain its transformation, using the amplitude, period, frequency, and midline questions as prompts for students to connect an equation with its graph.

What mistakes should I watch for when students complete this trigonometry review?

Watch for students confusing amplitude with period, frequency, or the midline when they read a sinusoidal equation or graph. Other common errors include assigning the wrong signs to trigonometric ratios by quadrant, mixing degree and radian measures, choosing an incorrect positive or negative angle, and describing a graph transformation without identifying its effect on the function.

How do I assign and grade this Franklin HS Algebra 2 Topic 7 Review worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for the multiple-choice, multiple-select, drawing, fill-in-the-blank, and open-ended items. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this trigonometry worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or font size to make the mixed-format items easier to read, including the graphing and open-ended prompts. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate for students working with the trigonometric equations and instructions.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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