Posted by Yuli on Monday, November 21, 2011 at 4:44am.
Let's go through this again.
θ is in the 3rd quadrant, so x and y are both negative, and the hypotenuse h = 13
sinθ = -5/13
cosθ = -12/13
Use these values in your half-angle and double-angle and sum/difference formulas.
sin 2θ = 2 sinθ cosθ = 2(-5/13)(-12/13) = 120/169
cos(θ-4π/3) = cosθ cos4π/3 + sinθ sin4π/3
= (-12/13)(-1/2) + (-5/13)(-√3/2)
= 12/26 + 5√3/26
sin θ/2 = √((1-cosθ)/2)
= √((1 + 12/13)/2)
= √(25/26)
Use this same method for all your other similar problems.
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