Question

Given angle theta is bigger than 0 and smaller than 360, determine two possible values of theta where each ration would be true.
a) cos theta= 0.6951
b)sin theta= -0.7571

Answer 1

Here is basically the simplest way to do these type of questions.
I will assume you are familiar with the CAST rule and have a calculator.

1. Use the absolute value of the given constant and use the inverse of the given trig ratio.
in this case, enter
2nd cos .6951 and press the = sign.
you should get 45.9648...
That is your "angle in standard position" , namely the first quadrant angle.

2. The cosine is positive in I and IV
so Ø = 45.965° or 360-45.965= 314.035°

b)
enter 2nd sin .7571 and press = to get
49.21°
BUT our sine was negative , so Ø had to be in III or IV
in III Ø = 180+49.21 = 229.21
in IV Ø = 360-49.21 = 310.79°

check these answers with your calculator, they work.