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Question

Find the value of sin15.


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Solution

Find the value of the trigonometric function using identities :

Given trigonometric function: sin15.

sin15can be expressed as, sin15=sin(45-30)


Using the identity sin(A-B)=sinAcosB-cosAsinB we can write,


sin(45-30)=sin45×cos30-cos45×sin30

We know that sin45=12,sin30=12,cos45=12, and cos30=32

By substituting the above values we get,

sin(45-30)=(12)(32)(12)(12)=322122=3122sin15=3122
Hence, the value of sin15is3122.


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