if tan theta = 3/4 and 180 degrees ≤ 0 ≤ 270 degrees determine with the aid of a complete sketch

Question

1. sin theta
2. cos(180 +theta)
3. angle theta

Answer 1

By "a complete sketch" they very likely want a right-angled triangle.
since tanØ = opposite/adjacent = 3/4 and the angle is in the third quadrant
y = -3 and x = -4
r^2 = 9 + 16 = 25
r = 5

sin Ø = -4/5

cos(Ø + 180)
= cosØcos180 - sinØsin180
= (cosØ)(-1) - 0
= - cosØ , you should know that identity
= -(-4/5)
= 4/5

Ø = 180 + tan^-1 (3/4)

= appr 216.9°