If CosA=3/5 and angle A is acute. Find each value. 1.) Sin A/2 2.) Cos2A 3.) Sin 2A

Answer 1

Since angle A is acute, sinA and cosA are both positive.

cosA = 3/5 and sinA = √[1 - sin²A) = 4/5

sin(A/2) = √[(1 - cosA) / 2] = √5/5 Note Since A is acute, so is A/2

cos(2A) = cos²A - sin²A = 9/25 - 16/25 = -7/25

sin(2A) = 2(sinA)(cosA) = 2(4/5)(3/5) = 24/25

Answer 2

cosa=.6

a=53.13°

Sin A/2 =.447213...

Cos2A=-.28

Sin 2A=.96