SOLUTION: Use half-angle formulas to find the exact values.
a. cos 15(degrees)
b. sin 20(degress)30'
I got {{{sqrt(3)}}}/2 for a and -{{{sqrt(2)}}}/2 for b which are wrong. What did I d
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Question 1159222: Use half-angle formulas to find the exact values.
a. cos 15(degrees)
b. sin 20(degress)30'
I got /2 for a and -/2 for b which are wrong. What did I do wrong?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm not sure what part b is trying to say because the notation is a bit strange.
I'll show you how to do part a
Half angle identity for cosine, when cosine is positive. Keep in mind that cos(15) is a positive value as the angle 15 degrees is in Q1 where cosine is positive.
Plug in x = 30
Replace cos(30) with sqrt(3)/2
Rewrite 1 as 2/2
Combine the upper fractions
Break up the square root
Simplify sqrt(4) into 2. This is as simplified as it gets.
-----------------------------------
Side note: if you use a calculator, you should find
(make sure your calculator is in degree mode)
both are approximations. Since we get the same approximation, this helps confirm the answer.
Another way to confirm the answer is to compute and you should get zero as a result (or some very small number due to rounding error). I'm using the idea that if , then
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