sin theta=-3/5 and theta is in the third quadrant, find the following: cos(theta+180/3)

Answer 1

since θ is in QIII, cosθ is also negative, and so is -4/5.

If you really meant what you wrote, then since 180/3 = 60, you want

cos(θ+60) = cosθ sinθ - cos60 sin60
= (-4/5)(-3/4) - (1/2)(√3/2)
= 3/5 - √3/4

If you meant cos (θ+180)/3 = cos(θ/3 + 60) then things are a bit harder

sinθ = -0.6 in QIII means θ=216.87

so, cos(θ/3 + 60) = cos(132.29) = -0.673

Answer 2

oops. misspoke on the first solution

cos(θ+60) = cosθ cos60 - sinθ sin60
= (-4/5)(√3/2) - (-3/5)(1/2)
= 3/10 - 2√3/5