Inverse trig review and derivative of inverse trig functions

We know $\sin^{-1}\left(1\right)=\frac{\pi}{2}$  because:

•  $\sin^{ }\left(\frac{\pi}{2}\right)=1$  

•  $\cos\frac{\pi}{2}=1$  

•  $\sin\left(1\right)=\pi$  

•  $\sin\left(\frac{1}{2}\right)=\pi$  

Tags

CCSS.HSF.TF.B.7

What is arctan(1)?

• $\pi$

• $\frac{\pi}{2}$

• $\frac{\pi}{4}$

• $\frac{\pi}{3}$

Tags

CCSS.HSF.TF.B.7

What is the derivative of arcsin( x) ?

• arccos(x)

• $\frac{1}{\sqrt{1-x^2}}$

• $\frac{1}{1+x^2}$

• - arccos(x)

What is the derivative of arctan( x) ?

• arccos(x)

• $\frac{1}{\sqrt{1-x^2}}$

• $\frac{1}{1+x^2}$

• - arccos(x)

Which of the following are equivalent?

• arcsin(x)

• $\sin^{-1}x$

• sin(1/x)

• arccosx

Tags

CCSS.HSF.TF.B.7

A right triangle has the opposite side of an angle theta as 4 units, and the adjacent side as 2 units. What is the angle theta in degrees?

• 22

• 34

• 55.2

• 63.4

Tags

CCSS.HSG.SRT.C.8

What is the derivative of arctan(3x)?

• $\frac{3}{1+9x^2}$

• $\frac{3}{1+3x^2}$

• $\frac{3}{\sqrt{1+9x^2}^{ }}$

• $\frac{1}{1+9x^2}$