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How do you use the angle sum identity to find the exact value of #sin285#?

Answer 1

#- sqrt(2 + sqrt3)/2#

Trig unit circle --> sin 285 = sin (-75 + 360) = sin (-75) Property of complementary arcs --> sin (-75) = sin (-15 + 90) = - cos 15 Next, find (cos 15) by using trig identity: #2cos^2 a = 1 + cos 2a# #2cos^2 (15) = 1 + cos 30 = 1 + sqrt3/2 = (2 + sqrt3)/2# #cos^2 15 = (2 + sqrt3)/4# #cos 15 = +- sqrt(2 + sqrt3)/2# Since cos 15 is positive then take the positive value only. Finally: sin 285 = - cos 15 = #- sqrt(2 + sqrt3)/2# Check by calculator: sin 285 = - 0.965 #- sqrt(2 + sqrt3)/2 = 1.93/2 = -0.965.# OK

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.