SOLUTION: 1. Apply a formula to find the exact value of the expression. Make sure to write down the formula first. Do not use a calculator. Simplify your answer completely. sin15°

Algebra ->  Trigonometry-basics -> SOLUTION: 1. Apply a formula to find the exact value of the expression. Make sure to write down the formula first. Do not use a calculator. Simplify your answer completely. sin15°      Log On


   



Question 1187016: 1. Apply a formula to find the exact value of the expression. Make sure to
write down the formula first. Do not use a calculator. Simplify your answer
completely.
sin15°
2. Apply a formula to find the exact value of the expression. Make sure to
write down the formula first. Do not use a calculator. Simplify your answer
completely.
cos11𝜋/12
Hello! For these two questions, I need help all the way through. I'm very stuck on what to do. Thank you!

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. Apply a formula to find the exact value of the expression. Make sure to
write down the formula first. Do not use a calculator. Simplify your answer
completely.
sin15°
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sin(15) = sin(30/2)sqrt
From "Half angle formulas" on Wikipedia:
sin%5E2%2830%2F2%29+=+%281-cos%2830%29%29%2F2
See Wikipedia Trigonometric functions to check your answer.
It's quite tedious and easy to make an error.
===========================================
cos(11𝜋/12) = cos(165)
= cos(120 + 45)
= cos(120)*cos(45) - sin(120)*sin(45)
= -0.5%2Asqrt%282%29%2F2+-+%28sqrt%283%29%2F2%29%2Asqrt%282%2F2%29
= -sqrt%282%29%2F4+-+sqrt%286%29%2F4
= -%28sqrt%282%29+%2B+sqrt%286%29%29%2F4