Can someone please help me to solve this question? I really confused how to solve the problem. It's emergency

Question

The question is that find an angle θ with 0 < θ< 360° or 0< θ <2 π that has the same sine value as:

a) π/3 b) 80 degrees c) 140 degrees d) 4π/3 e) 305 degrees

What type of formula I need to use it? The answers in the book it does not match with mines.

The book answer for that a) 2π/3 b) 100 degree c)40 degree d) 5π/3 and e) 235 degree

I really do not know what to do?

Answer 1

Problem a)

sin(π/3) = sin (60º) = sqrt(3) / 2 = √3 / 2

sin(60º + 60º) = sin (120º) = √3 / 2

120º = 2π/3

It helps if you have the unit circle diagram in front of you with all the sines and cosines for all the angles 0º, 30º, 45º, 60º, and 90º for each of the four quadrants.

Positive sine is the height above the x-axis.

The heights of +√3 / 2 applies to both 60º and 120º, or π/3 and 2π/3.

The other problems are similar.

Remember, sine is up and down, cosine is left and right.