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Question

How do I find the value of sin5π6.


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Solution

Calculate the value of sin5π6:

First, determine the sign of sin5π6.

5π6 can be rewritten as 5π6=π2+π3.

Thus 5π6 belongs to the second quadrant.

It is known that the values of sines are positive + in the second quadrant.

It is also known that, sin(π-x)=sin(x).

Thus, sin5π6=sinπ-π6=sinπ6=12.

Therefore, the value of sin5π6 is 12.


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