

Graphing Csc and Sec
Presentation
•
Mathematics
•
11th - 12th Grade
•
Hard
Joseph Anderson
FREE Resource
4 Slides • 12 Questions
1
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.

2
Multiple Choice
ACT Practice Problem:
What is the x-intercept of the graph of
-2
-1
0
1
2
3
Review of Secant and Cosecant
- Secant is the reciprocal of cosine
ie. sec θ = 1 / cos θ
- Cosecant is the reciprocal of sine
4
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
5
Multiple Choice
What is the period formula?
P = 2 π / b
P = π / 2b
P = π / b
6
Multiple Choice
What is the period of y = sec (6x)?
π
π / 2
π / 3
π / 6
7
Multiple Choice
What is the period of y = csc (1/3x)
π
2 π
3 π
6 π
8
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:
9
Multiple Choice
What is the equation for the vertical asymptote of y = sec (2x)?
x = π / 2 + π n/ 4
x = π / 4 + π n/ 2
x = π / 4 + 2 π n
x = π / 4 + π n/ 4
10
Open Ended
What is the equation for the vertical asymptote of y = csc (1/2x)?
11
Multiple Choice
Write an equation for a cosecant curve with vertical asymptotes at x = π / 3, 2 π / 3, and π
y = csc (x)
y = csc (3x)
y = csc (4x)
y = csc (6x)
12
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
13
Open Ended
(If in class) Graph y = csc (2x) and what are the asymptotes?
14
Multiple Choice
What is the equation of the graph?
y = sec (x + π /2)
y = sec (x - π /2)
y = csc (x + π /2)
15
Open Ended
Find the x-intercepts and vertical asymptotes of y = 5 sec (1/6x)
16
Multiple Choice
Exit Ticket:
Write the first 3 vertical asymptotes of y = csc (x)
x = 0, π , 2 π
x = 0, π / 2, π
x = π / 2, π , 3 π / 2
x = x = π / 2, 3 π / 2, 5 π / 2
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.

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