4.6 Day 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.

Multiple Choice

Which parent functions include the point (0, 1)?

• sine and cosecant

• cosine and secant

• cosine, secant, and tangent

• sine, cosecant, and cotangent

Multiple Choice

What is the amplitude of this function?

• 2
• 2π
• -2
• 1

Multiple Choice

Find the period of  $$y=\cos\left(3\theta+π/2\right)$$  

• 2π/3

• 6π

• 3π

• 4π/3

Multiple Choice

Find the amplitude of  $$y=-5\cos1/2\theta+π$$  

• 1

• -5

• 1/2

• 5

Multiple Choice

7.  What is the phase shift for y = 4cos(¹/₂x +π) - 2?

• left pi/2
• right pi/2
• right 2pi
• left 2pi

Multiple Choice

The __________ represents the distance from the baseline of sine/cosine to the max and min of the curve.

• Period

• Frequency

• Max/Min

• Amplitude

Multiple Choice

What is the period of the equation shown?

• 2π

• 4π

• π / 2

• π

Multiple Choice

What is the reciprocal function of sec?

• csc

• cos

• sin

• tan

Multiple Choice

The reciprocal of sine is

• cosine or cos

• secant or sec

• cosecant or csc

• arcsin or $$\sin^{-1}$$

Multiple Choice

If  $$\sin\theta=\frac{4}{5}$$  , then  $$\csc\theta=$$  

• $$\frac{4}{5}$$  

• $$-\frac{4}{5}$$  

• $$-\frac{5}{4}$$  

• $$\frac{5}{4}$$  

Review of Secant and Cosecant

Multiple Choice

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

• $$$$

• $$$$  / 2

• $$$$  / 3

• $$$$  / 6

Multiple Choice

What is the period formula?

• P = 2 $$\pi$$ / b

• P = $$$$ / 2b

• P = $$$$ / b

Multiple Choice

Phase shift means ...

• An up or down movement
• A left or right movement
• Height of graph
• ...set Phasers to stun

Multiple Select

Describe the transformations of y = - 6 csc ( 2x + π ) - 11

Select all that apply?

• down 11

• reflection over the x - axis

• phase shift = π/2 to the right

• period = pi

• Vertical Stretch is 6

Multiple Choice

What is the period of
y= 4 csc (5x)

• 2π/5
• π
• 5
• 5π

Multiple Choice

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

• $$\pi$$

• 2 $$$$

• 3 $$$$

• 6 $$$$

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:

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 $$$$ / 3, and $$$$

• y = csc (x)

• y = csc (3x)

• y = csc (4x)

• y = csc (6x)

Open Ended

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

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

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 $$$$

• x = 0, $$$$ / 2, $$$$

• x = $$$$ / 2, $$$$ , 3 $$$$ / 2

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