State the period, phase shift, and vertical shift 𝑓 𝑥 =−5 sin ( 1 4 𝑥−𝜋)

Period: 8pi Phase Shift: 4pi Vertical Shift: 0

State the period, phase shift, and vertical shift

Period: pi/4 Phase Shift: -2pi Vertical Shift: down 3

Write a single cosine function with… Amplitude = ½ x−axis reflection Period =4π Phase shift of π/2 radians -(1/2)cos(1/2(x-pi/2))

𝑦=− 1 2 cos⁡( 1 2 𝑥− 𝜋 2 )

Write a single sine function with… Amplitude = 3 Period =π Vertical shift up 2 units 3sin(2x)+2

Y=3sin(2x)+2

Give the domain and range in proper interval notation… 𝑓 𝑥 =−5 sin ( 1 4 𝑥−𝜋) D; all reals R: [-5,5]

Domain: −∞,∞ Range: [-5,5]

Give the domain and range in proper interval notation… 𝑓 𝑥 =2 cos 1 4 𝑥−𝜋 +3 D; all reals R: [1,5]

Domain: −∞,∞ Range: [1,5]

Sketch the graph of, and state domain and range 𝑓 𝑥 = cos −1 𝑥 D: [-1,1] R: [0,pi]

Sketch the graph of, and state domain and range 𝑓 𝑥 = sin −1 𝑥 D: [-1,1] R: [-pi/2,pi/2]

Graph one period of… f(x) = −2 cos( 𝟏 𝟑 x – π/6) − 1

Graph one period of… f(x) = −2 cos( 𝟏 𝟑 x – π/6) − 1

List the asymptotes of… f(x) = csc⁡(𝑥)

Asymptotes at 0+𝜋𝑘

What is the amplitude of 𝑓 𝑥 =−5 sin ( 1 4 𝑥−𝜋)

What is the amplitude of 𝑓 𝑥 =−5 sin ( 1 4 𝑥−𝜋) Amplitude is positive 5

Match each of the 6 trig functions with the other trig function that shares the same domain sin cos tan csc sec 𝑐𝑜𝑡

Match each of the 6 trig functions with the other trig function that shares the same domain Sin cos tan csc sec 𝑐𝑜𝑡

Solve for the principle values ( sin 𝑥)(1+ cos 𝑥)=0

Solve for the principle values ( sin 𝑥)(1+ cos 𝑥)=0 X=0 and 𝜋

Solve for all values between [0,2𝜋) 2 cos 2 𝑥 +4 cos 𝑥 +2=0

Solve for all values between [0,2𝜋) 2 cos 2 𝑥 +4 cos 𝑥 +2=0 { 𝜋}

Solve for all values between [0,2𝜋) 2 sin 2 𝑥= sin 𝑥

Solve for all values between [0,2𝜋) 2 sin 2 𝑥= sin 𝑥 {0, 𝜋 6 , 5𝜋 6 ,𝜋}