SOLUTION: Given that the exact value of sin pi/10 = -1+√5 divided by 4, for each question calculate the exact value of the expression. You may leave nested radicals in your answer, but

Algebra ->  Trigonometry-basics -> SOLUTION: Given that the exact value of sin pi/10 = -1+√5 divided by 4, for each question calculate the exact value of the expression. You may leave nested radicals in your answer, but      Log On


   

Question 1125840: Given that the exact value of sin pi/10 = -1+√5 divided by 4, for each question calculate the exact value of the expression. You may leave nested radicals in your answer, but rationalize any denominaters.
sin pi/5
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) sin%28pi%2F5%29+=+sin%28%282%2A%28pi%2F10%29%29%29+=+2sin%28pi%2F10%29cos%28pi%2F10%29

(2) cos%28pi%2F10%29+=+sqrt%281-sin%28pi%2F10%29%5E2%29

Substitute (2) into (1) and use the given value of sin(pi/10) to get


= %28%28-1%2Bsqrt%285%29%29%2F2%29%2Asqrt%281-%286-2%2Asqrt%285%29%29%2F16%29
= %28%28-1%2Bsqrt%285%29%29%2F2%29%2A%28sqrt%2810%2B2%2Asqrt%285%29%29%2F4%29
= %28%28-1%2Bsqrt%285%29%29%2Asqrt%2810%2B2%2Asqrt%285%29%29%29%2F8

Evaluating sin(pi/5) and that expression on a scientific calculator gives identical results, confirming the correctness of the expression.