Trig Equations Solutions

Question

Hi, I need help answering questions about the following graph:

f(x)=2 sin⁡x. I have plotted this on a graph already.

I just need help answering the following questions about it:

Use your graph to come up with a few solutions for the equation 2 sin⁡〖x=2.〗

Are there more solutions than the ones on the graph? Explain.

Thanks!!

Answer 1

Multiplying a trigononemetric function by scalar does not change the zeros/solutions.

The zeros of 2 sin x are the same as the zeros of sin x.

Multiplication by a scalar only changes the amplitude.

Answer 2

f(x) = 2sinx

x =0 + 180n where n= any integer, in degrees

or

x = 0 +npi radians where n= any integer

solutions are infinite

{..., -2pi, -pi, 0, pi, 2pi, ...} in radians

or {..., -360, -180, 0, 180, 360, ...} in degrees

graph sinx and 2sinx, the x intercepts are identical

2sinx is sinx stretched vertically by a factor of 2