Graphing Csc and Sec

4.6 Day 1 - Graphing Secant and Cosecant

Learning Objectives

-Understand how asymptote equations are found for secant and cosecant by finding when the function in the denominator is equal to 0.

-Graph and write secant and cosecant equations and identify the period and asymptote equations.

Multiple Choice

ACT Practice Problem:

What is the x-intercept of the graph of

$$f\left(x\right)=x^2-4x+4$$  ?

• -2

• -1

• 0

• 1

• 2

Review of Secant and Cosecant

- Secant is the reciprocal of cosine
ie. sec $\theta$  = 1 / cos $\theta$   

- Cosecant is the reciprocal of sine

ie. csc $\theta$  = 1 / sin $\theta$   

Vertical Asymptotes of Secant, Cosecant and Tangent

How to find vertical asymptotes of Sec, Csc, Cot:

https://www.brightstorm.com/math/precalculus/trigonometric-functions/asymptotes-of-secant-cosecant-and-cotangent/

Cosecant and Secant vs Sine and Cosine Graphing on Desmos link:

https://www.desmos.com/calculator/jztjnself7

Multiple Choice

What is the period formula?

• P = 2 $$\pi$$ / b

• P = $\pi$ / 2b

• P = $\pi$ / b

Multiple Choice

What is the period of y = sec (6x)?

•  $\pi$ 

•  $\pi$  / 2

•  $\pi$  / 3

•  $\pi$  / 6

Multiple Choice

What is the period of y = csc (1/3x)

• $$\pi$$

• 2 $\pi$

• 3 $\pi$

• 6 $\pi$

Vertical Asymptote Review

y = 1/(x-2) is graphed to the right. There is a V.A. at x = 2.

Why is there a vertical asymptote at x = 2?

We apply this to trigonometric equations on the following slides:

Multiple Choice

What is the equation for the vertical asymptote of y = sec (2x)?

• x = $$\pi$$ / 2 +  $$\pi$$ n/ 4

• x = $\pi$ / 4 +  $\pi$ n/ 2

• x = $\pi$ / 4 + 2 $\pi$ n

• x = $\pi$ / 4 +  $\pi$ n/ 4

Open Ended

What is the equation for the vertical asymptote of y = csc (1/2x)?

Multiple Choice

Write an equation for a cosecant curve with vertical asymptotes at x = $$\pi$$ / 3, 2 $$\pi$$ / 3, and $$\pi$$

• y = csc (x)

• y = csc (3x)

• y = csc (4x)

• y = csc (6x)

Multiple Choice

Which is the correct equation for the graph given

• y = sec (x) + 1

• y = sec (x) - 1

• y = csc (x) + 1

• y = csc (x) - 1

Open Ended

(If in class) Graph y = csc (2x) and what are the asymptotes?

Multiple Choice

What is the equation of the graph?

• y = sec (x + $\pi$ /2) 

• y = sec (x - $\pi$ /2) 

• y = csc (x + $\pi$ /2) 

Open Ended

Find the x-intercepts and vertical asymptotes of y = 5 sec (1/6x)

Multiple Choice

Exit Ticket:

Write the first 3 vertical asymptotes of y = csc (x)

• x = 0, $$\pi$$ , 2 $$\pi$$

• x = 0, $\pi$ / 2, $\pi$

• x = $\pi$ / 2, $\pi$ , 3 $\pi$ / 2

• x = x = $\pi$ / 2, 3 $\pi$ / 2, 5 $\pi$ / 2