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Inverse Trig Graphs - Printable Mathematics Worksheets grade 10 - Wayground

Inverse Trig Graphs

16 questions

9th - 12th Grade

Mathematics

Inverse Trig Graphs is a free printable mathematics worksheet for Grades 9–12 that builds students’ ability to identify and interpret inverse sine and inverse cosine graphs. It focuses on switching x and y to create an inverse function, matching points to the appropriate graph, recognizing arcsin and arccos notation, and distinguishing inverse functions from reciprocal functions such as cosecant and secant. The 16-question worksheet combines one dropdown item, two drag-and-drop image activities, and 13 multiple-choice questions. Students identify equations from graphs, select graphs from equations, and determine the domains and ranges of y = sin⁻¹x and y = cos⁻¹x, including [-1, 1], [-π/2, π/2], and [0, π]. This free printable worksheet includes a complete answer key for instruction, independent practice, or assessment.

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Worksheets

Inverse Trig Graphs

Total questions: 16

Name
Class
Date
1.

The best strategy for creating a(n) ​ (a)   function is to switch the x and the ​ (b)  

Choose from the below words
inverse
y
cosine
tangent
h
k
2.

Drag each point to the function that it should be on

a) (1,π2)\left(1,\frac{\pi}{2}\right)
b) (π2, 1)\left(\frac{\pi}{2},\ 1\right)
1
2
1)
2)
3.

Drag each point to the function that it should be on (the dotted line is arccos and the solid line is cos)

a) (π3, 12)\left(\frac{\pi}{3},\ \frac{1}{2}\right)
b) ( 12,π3)\left(\ \frac{1}{2},\frac{\pi}{3}\right)
1
2
1)
2)
4.
y = arcsin x is the same graph as which of the following?
a)
y= csc x
b)
y = sec x
c)
y = sin-1 x
d)
y = csc-1 x
5.
y = arccos x is the same graph as which of the following?
a)
y= cos x
b)
y = sec x
c)
y = sec-1 x
d)
y = cos-1 x
6.
This is the equation of which graph?
a)
y = sin-1 x
b)
y = cos-1 x
c)
y = sec x
d)
y = csc x
7.
This is the equation of which graph?
a)
y = sin-1 x
b)
y = cos-1 x
c)
y = sec x
d)
y = csc x
8.

What is the range of the cos-1 graph?

a)

(-∞,∞)

b)

[-1, 1]

c)

(-π/2, π/2)

d)

[0,π]

9.

What is the domain of the cos-1 graph?

a)

(-∞,∞)

b)

[-1, 1]

c)

(-π/2, π/2)

d)

[0,π]

10.

What is the domain of the sin-1 graph?

a)

(-∞,∞)

b)

[-1, 1]

c)

(-π/2, π/2)

d)

[0,π]

11.

What is the range of the sin-1 graph?

a)

(-∞,∞)

b)

[-1, 1]

c)

[-π/2, π/2]

d)

[0,π]

12.

The black dotted line is  y=sin⁡−1xy=\sin^{-1}x .


Which graph shows  y=2sin⁡−1xy=2\sin^{-1}x ?

a)

A

b)

B

c)

C

d)

D

13.

The black dotted line is  y=sin⁡−1xy=\sin^{-1}x .


Which graph shows  y=sin⁡−12xy=\sin^{-1}2x  ?

a)

A

b)

B

c)

C

d)

D

14.

The black dotted line is  y=cos⁡−1xy=\cos^{-1}x .


Which graph shows  y=12cos⁡−1xy=\frac{1}{2}\cos^{-1}x  ?

a)

A

b)

B

c)

C

d)

D

15.

The black dotted line is  y=cos⁡−1xy=\cos^{-1}x .


Which graph shows  y=cos⁡−1(x2)y=\cos^{-1}\left(\frac{x}{2}\right)  ?

a)

A

b)

B

c)

C

d)

D

16.

Which function best describes the following graph?

a)

y=3sin⁡−12xy=3\sin^{-1}2x  

b)

y=32sin⁡−12xy=\frac{3}{2}\sin^{-1}2x

c)

y=3sin⁡−1x2y=3\sin^{-1}\frac{x}{2}

d)

y=32sin⁡−1x2y=\frac{3}{2}\sin^{-1}\frac{x}{2}

Answer Key

Inverse Trig Graphs

Total questions: 16

1.
inverse, y
2.
a
b
3.
a
b
4.
c) y = sin-1 x
5.
d) y = cos-1 x
6.
b) y = cos-1 x
7.
a) y = sin-1 x
8.
d)

[0,π]

9.
b)

[-1, 1]

10.
b)

[-1, 1]

11.
c)

[-π/2, π/2]

12.
b)

B

13.
d)

D

14.
b)

B

15.
a)

A

16.
c)

y=3sin⁡−1x2y=3\sin^{-1}\frac{x}{2}

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FAQs

What does the Inverse Trig Graphs worksheet cover?

This worksheet helps students identify and interpret graphs of y = sin⁻¹x and y = cos⁻¹x. Its dropdown, drag-and-drop image, and multiple-choice items ask students to switch x and y when forming an inverse, match points to inverse graphs, distinguish arcsin and arccos from reciprocal functions, and identify the correct domains and ranges.

How can I use this worksheet to teach inverse sine and cosine graphs?

Introduce the worksheet by reviewing how switching x and y produces an inverse and how inverse graphs relate to the original function. Use the two drag-and-drop activities to have students justify point placement, then use the equation-and-graph multiple-choice questions to connect notation with visual features. Finish by asking students to explain why the domain and range values for arcsin and arccos differ.

What mistakes should I watch for when students complete this inverse trig graph worksheet?

Watch for students treating sin⁻¹x as 1/sin x or confusing cos⁻¹x with sec x; the multiple-choice items specifically test these notation differences. Students may also reverse the domain and range, select [-1, 1] as the range of an inverse graph, or confuse the principal ranges [−π/2, π/2] and [0, π]. In the point-matching and graph-identification items, check that they use the inverse relationship rather than matching points to the original sine or cosine graph.

How do I assign and grade the Inverse Trig Graphs worksheet?

On Wayground, you can assign Inverse Trig Graphs as a printable PDF or as a digital quiz, with the same inverse-function graphing practice in either format. The worksheet includes a complete answer key for checking the dropdown, drag-and-drop, and multiple-choice responses. For printable submissions, scan student work with the Wayground for Teachers app to support grading.

How can I differentiate this inverse trig graphs worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the graph-identification and point-matching items are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support access to the inverse sine and cosine questions.

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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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