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

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

3. State the period, phase shift, and vertical shift

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

5. 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))

6. 𝑦=− 1 2 cos⁡( 1 2 𝑥− 𝜋 2 )

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

8. Y=3sin(2x)+2

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

10. Domain: −∞,∞ Range: [-5,5]

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

12. Domain: −∞,∞ Range: [1,5]

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

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

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

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

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

20. Asymptotes at 0+𝜋𝑘

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

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

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

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

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

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

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

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

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

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