Question

Question #1:

If cos x = 7/25, and 0 < x < pi/2, what is sin(x - 3pi/2)

question #2:
if tan x = sqrt(3), and 180(degrees) < x < 270(degrees), what is sin(x - 210degrees)?

Answer 1

Try this solution (note, this is not the only way):

Q1: if sin(x- 3pi/2)=-sin(3pi/2- x)=--cosx=cosx, then sin(x- 3pi/2)=cosx and sin(x- 3pi/2)=7/25.

Q2: if tan(x)=√3 and x∈(180°;270°), then x=arctan√3+180°=60+180=240°.

If x=240°, then sin(x-210°)=sin30°=0.5.