Question

Q#1. If cos = -1/2 and 90 < x < 180, what is sin(x - 30)

q#2. if tan x = -sqrt(3)/3, and (3pi)/2 < x < 2pi, find sin(x + pi/6)

please help and thank you!!

Answer 1

Try this solution (this is not the only way!):

Q1: if cosx=-0.5 and x∈(90;180), it means x=120°.

So, sin(x-30)=sin(120-30)=sin90°=1.

answer: 1.

Q2: it tgx= -1/√3 and x∈(270°;360°), it means x=330°.

So, sin(x+30)=sin(330+30)=sin360°=0.

answer: 0.