How do I write a sine function with this info?

Question

a. amplitude: 35.7, period: π/4
b. amplitude: 0.34, period: 0.75π
c. amplitude: 16, period: 30π
I need steps too so I know how do do this, please.

... in radians not degrees.

y= ...sin(...x)

Answer 1

Examples
Function_____Period___Amplitude
sin x_________2π_______1
sin 2x________π________1
3sin 4x_______π/2______3
5sin 8x_______π/4______5

Question
35.7sin 8x_____π/4_____35.7
0.34sin(8/3)x)__3π/4____0.34
16sin(1/15)x___30π_____16

Answer 2

The general equation of any sine wave will be in the format of :
y = A*sin (2*pi*t/T) = A*sin(2*pi*n*t)
where:
A : Amplitude of the sine wave.
pi : 3.141596....
T: period of wave in seconds.
n : Frequency of the wave (in Hz).
t: : the time variable.

So the answer to the question is very simple:
Just put the valuse at the right place.

Here are the answers:

a. A = 35.7 and T = pi/4
so : y = 35.7 * sin ( 2*pi*t/(pi/4) )
y = 35.7*sin (8t)

b. A = 0.34 T = 3pi/4
hence y = 0.34*sin ( 8/3 *t)

c. A = 16 T = 30pi
hence, y = 16* sin ( 1/15 *t)

Answer 3

y=35.7sin8x
y=0.34sin8x/3
y=16sinx/15
amplitude is the coefficient in front of sin
period is 2pi/the coefficient in front of x

Answer 4

35.7sin(x/8)

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