Lesson Secant, Cosecant, and Cotangent Functions

Trigonometric Functions (All Six Trigonometric )

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Graphing Secant and Cosecant

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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

$$\sec x\ =\ \frac{1}{\cos x}$$  

Find 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 = ?

• $$\pi$$  

• $$\frac{\pi}{2}$$  

• $$2\pi$$

• $$\frac{3\pi}{2}$$  

Open Ended

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  and y = sin 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

Multiple Choice

Which trig function is graphed?

• y=secx

• y=cscx

• y=tanx

• y=sinx

• y=cosx

Multiple Choice

Which parent function is graphed?

• y=tanx

• y=cotx

• y=sinx

• $$y=\tan^{-1}x$$

• y=cosx

Multiple Choice

Which trig function is graphed above?

• secant

• cotangent

• cosecant

• tangent

Multiple Select

Which of these trig functions has a period of

$$2\pi$$  ?

• $$y=\sin x$$  

• $$y=\cos x$$  

• $$y=\tan x$$  

• $$y=\cot x$$  

• $$y=\csc x$$

Multiple Choice

$$\sec\theta=?$$  

• $$\frac{x}{r}$$  

• $$\frac{y}{r}$$  

• $$\frac{r}{y}$$  

• $$\frac{r}{x}$$  

Multiple Choice

$$\csc\theta=?$$  

• $$\frac{x}{r}$$  

• $$\frac{y}{r}$$  

• $$\frac{r}{y}$$  

• $$\frac{r}{x}$$