Theta = x

Question

Question: Given angle x, where 0degrees <= x <= 360 degrees, solve for x to the nearest degree.
b) sin(x + 20degrees) = 0.2045
c) tan(90degrees - 2x) = 1.6443
I am confused as to where 148 degrees comes from in question b and how there are 4 possibilities in question c.

Answer 1

b) sin(x + 20degrees) = 0.2045
Using your calculator you should get:
x+20° = 11.8 in quadI OR x+20 = 168.2 in quadII
x = -8.2° , but our domain was 0 ≤ x ≤ 360° , so we reject that answer
or
x = 168.2-20 = 148.2° , the given answer

c) tan(90degrees - 2x) = 1.6443
90° -2x = 58.7° in quad I or 90-2x = 238.7° in quad III
-2x = -31.3 or -2x = 148.7
x = 15.65 or x = - -74.35° <----- not admissable

now the period of tanØ = 90°
so adding multiples of 90 to any of our answers will yield a new one, so ...
x = - 74.35 + 90 = 15.65°
x = 15.65°
x = 15.65 + 90 = 105.65°
x = 105.65+90 = 195.65°
x = 195.65+90 = 285.65 <------ there are your 4 answers

15.65, 105.65, 195.65 , 285.65