HPC Section 4.6 Sec & Csc Day 1

Precalculus Section 4.6

Trigonometric Functions

Day 1

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Graphing Secant and Cosecant

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Multiple Choice

When graphing y = csc x, what will the zeros of y = sin x become?

• asymptotes

• zeros

• minimums

• maximums

Multiple Choice

When graphing y = csc x, where will y = sinx and y = csc x touch?

(In other words, where are sin x and csc x equal?)

• $$x=\pi\cdot n$$

• $$x=\frac{\pi}{2}+\pi\cdot n$$

• $$x=\frac{\pi}{2}\cdot n$$

• $$x=\frac{\pi}{4}\cdot n$$

The reason we spent so much time on sine and cosine is so that cosecant and secant would be easier.

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Reciprocal functions

When graphing cosecant, graph sine first.
When graphing secant, graph cosine first.

It really is that simple.

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Reciprocal functions

Multiple Choice

Reciprocal Function Graphs

$$\csc x\ =\ \frac{1}{\sin x}$$  

When sin x = 1, what is csc x = ?

• 1

• 0

• undefined

• -1

Multiple Choice

Reciprocal Function Graphs

$$\sec x\ =\ \frac{1}{\cos x}$$  

When $$x\ =\ \frac{\pi}{2}$$   what is sec x = ?

• 1

• 0

• undefined

• -1

Multiple Select

Reciprocal Function Graphs

Because

$$\sec x\ =\ \frac{1}{\cos x}$$  and $$\tan x\ =\ \frac{\sin x}{\cos x}$$  

They are undefined at the same places where x = ?

• $$\pi$$  

• $$\frac{\pi}{2}$$  

• $$2\pi$$

• $$\frac{3\pi}{2}$$  

Fill in the Blanks

When graphing these reciprocal functions like sec x and csc x and for the ratio functions like tan x and cot x, each time the denominator equals zero (the function is undefined) there will be in a(n)

on the graph.

y = sin x

y = csc x

y = csc x

Multiple Choice

$$y\ =\ 2\sin\ \left(x+\frac{\pi}{4}\right)$$  

What is the amplitude of the graph ?

• 2

• $$\pi$$  

• 4

• None

Multiple Choice

$$y\ =\ 2\sin\ \left(x+\frac{\pi}{4}\right)$$  

What is the period of the graph ?

• $$2\pi$$  

• $$\pi$$  

• $$4\pi$$  

• $$\frac{\pi}{4}$$  

Multiple Choice

$$y\ =\ 2\sin\ \left(x+\frac{\pi}{4}\right)$$  

What is the phase shift of the graph?

• $$2\pi$$ left

• $$\pi$$ left

• $$4\pi$$ left

• $$\frac{\pi}{4}$$ left

Draw

Graph $$y\ =\ 2\ \sec\frac{1}{2}\left(x-\pi\right)+1$$

(Graph cosine first)

Homework Day 1 - Secant and Cosecant

• Page 311

• #7, 8, 15, 17, 20, 23, - -> Graph 21 in your calculator just to see it.

• Why does #21 look like that?