Would someone verify these answers.

Question

1. A person waves his hand back and forth, where their finger tips move past the starting position 4 cm in each direction. If he waves 20 times every 15s, what sine equation models the movement of the hand if the hand starts in the upright position and the right direction will be taken as positive?

a)y=4sin(20pi/15 x t)
b)y=4sin(30pi/20 x t)
c)y=4sin(40pi/15 x t)
c)y=8sin(30pi/20 x t)

Answer: A
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2. Which of the six trig functions are positive in quad III?

Ans: Tangent and cotangent
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3. What is the exact value of sin(3pi/2)?

Answer: 3pi/2=270 degree, equals to -1

Therefor exact value -1.

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Answer 1

1.
If he waved once every second, the frequency would be 1. you'd have sin(2πt).
If he waved n times, you'd have sin(2πnt).
Would you like to change your answer to C?

2. ok

3. ok

Answer 2

Hmm. If a wave is defined as moving away from the starting point and back, your A answer is correct.

If a wave is defined as a complete cycle away and back in each direction, then the answer would be C.

Answer 3

I am confused for number 3

Answer 4

sin(270) = sin(90+180) = sin90cos180 + cos90sin180 = 1(-1) + 0*0 = -1

or, at 270 deg, y=-1, x=0, r=1

sin = y/r = -1/1 = -1