Suppose \(\theta = \frac{11\pi}{12}\). How do you use the sum identity to find the exact value of \(\sin \theta\)?
Answer (2)
The better way is, first we have to find the equivalent in degrees
2 π = 360 \º
12 11 π = 345 \º
now we can change this value to − 15 \º
how do we get an angle like this?!
30 \º − 45 \º = − 15 \º
then
s in ( 30 \º − 45 \º ) = s in ( 30 \º ) ∗ cos ( 45 \º ) − s in ( 45 \º ) ∗ cos ( 30 \º )
\begin{Bmatrix}sin(30\º)&=&\frac{1}{2}\\\\sin(45\º)&=&cos(45\º)&=&\frac{\sqrt{2}}{2}}\end{matrix}\\\\cos(30\º)&=&\frac{\sqrt{3}}{2}\end{matrix}
now we replace this values
s in ( − 15 \º ) = 2 1 ∗ 2 2 − 2 2 ∗ 2 3
s in ( − 15 \º ) = 4 2 − 4 6
s in ( − 15 \º ) = s in ( 345 \º ) = 4 2 − 6
To find sin ( 12 11 π ) , we use the sine sum identity. By expressing 12 11 π as 3 π + 4 π , we can find that sin ( 12 11 π ) = 4 6 + 2 .
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