SOLUTION: Given sin 30°= 1/2, use trigonometric identities to find the exact value of: A: cos 60° B: cosē30° C: csc π/6 D: sec π/3

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Question 969094: Given sin 30°= 1/2, use trigonometric identities to find the exact value of:
A: cos 60°
B: cosē30°
C: csc π/6
D: sec π/3
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Given sin 30°= 1/2, use trigonometric identities to find the exact value of:
A: cos 60°
Use cos%28theta%29=sin%28%2290%B0%22-theta%29

cos(60°) = sin(90°-60°) = sin(30°) = 1%2F2

B: cosē30°
Use cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1 written as cos%5E2%28theta%29=1-sin%5E2%28theta%29

cosē30° = 1 - sinē30° = 1 - %281%2F2%29%5E2 = 1 - 1%2F4 = 3%2F4

C: csc π/6
Use csc%28theta%29=1%2Fsin%28theta%29

csc%28pi%2F6%29%22%22=%22%22csc%28+expr%28pi%2F6%29%2Aexpr%28%22180%B0%22%2Fpi%29%29%22%22=%22%22csc%28%2230%B0%22%29%22%22=%22%221%2Fsin%28%2230%B0%22%29%22%22=%22%221%2Fexpr%281%2F2%29%22%22=%22%221%2Aexpr%282%2F1%29%22%22=%22%222

D:
sec π/3
Use sec%28theta%29=csc%28pi%2F2-theta%29 and the results of part C

sec%28pi%2F3%29%22%22=%22%22csc%28pi%2F2-pi%2F3%29%22%22=%22%22csc%283pi%2F6-2p%2F6%29%22%22=%22%22csc%28pi%2F6%29%22%22=%22%222

Edwin