6.1 - Graphing Secant and Cosecant

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.

Review of Secant and Cosecant

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 +  $$k\pi$$ / 4

• x = $$\pi$$ / 4 +  $$k\pi$$ / 2

• x = $$\pi$$ / 4 + 2 $$k\pi$$

• x = $$\pi$$ / 4 +  $$k\pi$$ / 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) 

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