HPC Section 4.7 Inverse Trig Functions Day 2

Precalculus Section 4.7 Inverse Trig Functions Day 2

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Multiple Choice

Graph y = arctan x with your calculator.

What is the domain of the function?

• (-1, 1)

• All Reals

• $$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$$  

• $$\left(-\pi,\ \pi\right)$$  

Multiple Choice

Look at the graph y = arctan x on your calculator.

What is the range of the function?

• (-1, 1)

• All Reals

• $$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$$  

• $$\left(-\pi,\ \pi\right)$$  

y = tangent x

What would the restriction need to be for this graph to pass the horizontal line test?

Discuss with a neighbor

Multiple Choice

Evaluate:

The answer must be within the range for the inverse function.

arctan (-1)

• $$-\frac{\pi}{4}$$  

• $$\frac{3\pi}{4}$$  

• $$\frac{5\pi}{4}$$  

• $$-\frac{\pi}{2}$$  

Multiple Choice

Evaluate:

The answer must be within the range for the inverse function.

arccos (-1)

• $$-\pi$$  

• $$\pi$$  

• $$\frac{\pi}{2}$$  

• $$-\frac{\pi}{2}$$  

Multiple Choice

Evaluate:

The answer must be within the range for the inverse function.

$$\tan^{-1}\left(0\right)$$  

• $$-\pi$$  

• $$\pi$$  

• $$0$$  

• $$-\frac{\pi}{2}$$  

• $$\frac{\pi}{2}$$  

Composite functions

Fill in the Blanks

$f\left(x\right)=\sqrt{x^2}$   Think about this function.   Evaluate if x = 4.

Fill in the Blanks

$f\left(x\right)=\sqrt{x^2}$   Think about this function.   Evaluate if x = 7.

Fill in the Blanks

$f\left(x\right)=\sqrt{x^2}$  

Think about this function.  

Evaluate if x = -2.

Multiple Choice

Evaluate:

$$\sin\left(\sin^{-1}\left(\frac{1}{2}\right)\right)$$  

• $$\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{\pi}{6}$$  

• $$\frac{\pi}{3}$$  

Multiple Choice

Evaluate:

$$\cos\left(\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)\right)$$  

• $$\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{\pi}{6}$$  

• $$\frac{\pi}{3}$$  

Multiple Choice

Evaluate:

$$\cos^{-1}\left(\cos\left(\frac{\pi}{4}\right)\right)$$  

• $$1$$  

• $$\frac{\sqrt{2}}{2}$$  

• $$\frac{\pi}{4}$$  

• $$\frac{\pi}{2}$$  

Multiple Choice

Evaluate:

$$\sin^{-1}\left(\sin\left(90\degree\right)\right)$$

• $$1$$  

• $$\pi$$  

• $$90\degree$$  

• $$0\degree$$  

Multiple Choice

Evaluate:

$$\sin^{-1}\left(\sin\left(210\degree\right)\right)$$  

• $$30\degree$$  

• $$60\degree$$  

• $$-30\degree$$  

• $$150\degree$$  

• $$210\degree$$  

So why is this not 210?

Let's evaluate from the inside out.
What is sin (210) ?

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Multiple Choice

Evaluate:

$$\sin^{-1}\left(\sin\left(\frac{3\pi}{4}\right)\right)$$  

• $$\frac{\pi}{4}$$   

•   $$-\frac{\pi}{4}$$   

• $$\frac{\pi}{6}$$  

• $$\frac{\pi}{3}$$  

Multiple Choice

Evaluate:

$$\sin\left(\cos^{-1}\left(\frac{1}{2}\right)\right)$$  

• $$\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{\pi}{6}$$  

• $$\frac{\pi}{3}$$  

Multiple Choice

Evaluate:

$$\cos\left(\tan^{-1}\left(1\right)\right)$$  

• $$\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{\sqrt[]{2}}{2}$$  

• $$\frac{\pi}{4}$$  

• $$1$$  

Multiple Choice

Evaluate:

$$\cos\left(\cos^{-1}\left(\pi\right)\right)$$  

• $$\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{\pi}{6}$$  

• $$\frac{\pi}{3}$$  

• not possible

Homework Day 2

• Page 322 - 325

• #1, 2, 8, 9, 13, 14, 18, 20, 24, 28, 32, 46, 53 - 59 odd

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