SOLUTION: Can you do this sin(1/2(theta))=1/2sin(theta)? If the answer is yes, prove using identities. If the answer is no, give an example of a particular theta which this fails.

Question 572966: Can you do this sin(1/2(theta))=1/2sin(theta)?
If the answer is yes, prove using identities.
If the answer is no, give an example of a particular theta which this fails.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let's assume that theta equals 90 degrees.
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If theta equals 90 degrees, then (1/2)*(theta) is equal to 45 degrees, and sin(45) is approximately 0.7071.
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Next, what is sin(theta) for theta = 90 degrees?. The answer to that is +1. This means that if theta equals 90 degrees, then:
.
(1/2)* sin(theta) = (1/2)*(+1) = 1/2 = 0.5000
.
Therefore, we can say that if theta equals 90 degrees then:
.
sin((1/2)*theta) = 0.7071 and
1/2*sin(theta) = 0.5000
.
With this example, you can now say that it is not always true that:
.
sin(1/2(theta))=1/2sin(theta)
.
Hope this helps you to understand a way this problem can be answered and what the answer is.
.
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