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Name _____________________ Review B MA 133
Write your answer, including units, on the line provided. Show work on this paper or lose credit. NOT ACCEPTED LATE Due October 26
- For each of the following functions, give the amplitude, period, phase shift, vertical shift, and graph over the indicated interval.
a. (^)
3 sin π y x , Graph one complete cycle
A = ___ p = ___ PS = ____ VS = _____
b. y = 2 −cos( π x ) over − 2 ≤ x ≤ 4
A = ___ p = ___ PS = ____ VS = _____
c. (^)
2 sin 3
π y x , Graph one complete cycle
A = ___ p = ___ PS = ____ VS = _____
d. y = 2 cos( 3 x ), Graph one complete cycle
A = ___ p = ___ PS = ____ VS = _____
- Simplify each of the following expressions: Write your answer in exact radians.
a. (^)
cos 1 , angle in QIII
b. cot −^1 ( − 1 ), angle in QIV
_________
_________
- Simplify each of the following expressions with EXACT answers
a. (^)
cos cot^1
________
b. (^)
x
sin cos^1
________
- Prove each of the following identities. You may use any of the formulas provided. a. (1 – cos A) (1 + cos A) = sin^2 A
b. A A
A
csc cos
cot
c. 2
1 cos( 2 ) sin 2
A
A
b. cos 2B
______
c. 2
cos
A
______
d. cos ( A – B)
______
- Give an equation to fit the graph. Give the amplitude, period, phase shift and vertical shift:
a. A = ___ p = ___ PS = ____ VS = ____
Eqn:______________________________
b. A = ___ p = ___ PS = ____ VS = ____
Eqn:______________________________
sin^2 x + cos^2 x = 1
1 + tan^2 x = sec^2 x
1 + cot^2 x =csc^2 x
sin (A + B) = sin A cos B + sin B cos A
sin (A – B) = sin A cos B – sin B cos A
cos (A + B) = cos A cos B – sin A sin B
cos (A – B) = cos A cos B + sin A sin B
sin 2x = 2 sin x cos x cos 2x = cos^2 x – sin^2 x = 2 cos^2 x - 1 = 1 – 2 sin^2 x
1 cos 2
sin
A − A
1 cos 2
cos
A + A
