Free Printable Daily Challenge 1: Odd-and-Even and Cofunction Identities

1.

Consider the function $f\left(x\right)=\sin^{-1}x$ .

Which of the following is true?

a)

$f\left(-x\right)=f\left(x\right)$

even function

b)

$f\left(-x\right)=-f\left(x\right)$

odd function

c)

neither odd nor even function

2.

Consider the function $f\left(x\right)=\tan^{-1}x$ .

Which of the following is true?

a)

$f\left(-x\right)=f\left(x\right)$

even function

b)

$f\left(-x\right)=-f\left(x\right)$

odd function

c)

neither odd nor even function

3.

Consider the function $f\left(x\right)=\cos^{-1}x$ .

Which of the following is true?

a)

$f\left(-x\right)=f\left(x\right)$

even function

b)

$f\left(-x\right)=-f\left(x\right)$

odd function

c)

neither odd nor even function

4.

What are the colors of the graphs of $y=\sin^{-1}x$ and $y=\tan^{-1}x$ ?

a)

red and blue

b)

green and blue

c)

red and green

5.

The graphs of $y=\sin^{-1}x$ and $y=\tan^{-1}x$ are

a)

symmetric with respect to the x-axis

b)

symmetric with respect to the y-axis

c)

symmetric with respect to the origin

d)

not symmetric

6.

The graph of $y=\cos^{-1}x$ is

a)

symmetric with respect to the x-axis

b)

symmetric with respect to the y-axis

c)

symmetric with respect to the origin

d)

not symmetric

7.

The graph of $y=\sin x$ can be described as the graph of $y=\cos x$ shifted

a)

$\frac{\pi}{2}$ to the right

b)

$\frac{\pi}{2}$ to the left

c)

$\pi$ to the right

d)

$\pi$ to the left

8.

This means we can describe sine as

a)

$\sin x=\cos\left(x+\frac{\pi}{2}\right)$

b)

$\sin x=\cos\left(x-\frac{\pi}{2}\right)$

c)

$\sin x=\cos\left(x+\pi\right)$

d)

$\sin x=\cos\left(x-\pi\right)$

9.

Since

a)

sine is an odd function

b)

sine is an even function

c)

cosine is an odd function

d)

cosine is an even function

10.

We can derive the Cofunction Identity

a)

$\sin\left(\frac{\pi}{2}-x\right)=\cos x$

b)

$\cos\left(\frac{\pi}{2}-x\right)=\sin x$

c)

$\sin\left(\frac{\pi}{2}+x\right)=\cos x$

d)

$\cos\left(\frac{\pi}{2}+x\right)=\sin x$

Daily Challenge 1: Odd-and-Even and Cofunction Identities

Total questions: 10

Worksheet time: 15mins

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