Question

What's the exact value of sin 7/12?

Answer 1

The exact value of sin(7π12) sin ( 7 π 12 ) is √2+√64 2 + 6 4 .

Answer 2

Answer:

C

Step-by-step explanation:

using the addition formula for sine

sin(A + B) = sinAcosB + cosAsinB

note that $\frac{7\pi }{12}$ = $\frac{\pi }{3}$ + $\frac{\pi }{4}$ , then

sin $\frac{7\pi }{12}$

= sin($\frac{\pi }{3}$ + $\frac{\pi }{4}$ )

= sin$\frac{\pi }{3}$cos$\frac{\pi }{4}$ + cos$\frac{\pi }{3}$sin$\frac{\pi }{4}$

= ( $\frac{\sqrt{3} }{2}$ × $\frac{\sqrt{2} }{2}$ ) + ($\frac{1}{2}$ × $\frac{\sqrt{2} }{2}$ )

= $\frac{\sqrt{6} }{4}$ + $\frac{\sqrt{2} }{4}$

= $\frac{\sqrt{2}+\sqrt{6} }{4}$