Question

I need help figuring out what I did wrong

Answer 1

Answer:

d

Step-by-step explanation:

Answer 2

Answer:

D

Step-by-step explanation:

Using the addition formula for sine

sin(a + b) = sinacosb + cosasinb

and the exact values

sin($\frac{\pi }{4}$ ) = cos($\frac{\pi }{4}$ ) = $\frac{\sqrt{2} }{2}$ , cos($\frac{\pi }{6}$) = $\frac{\sqrt{3} }{2}$ , sin($\frac{\pi }{6}$) = $\frac{1}{2}$

Note that $\frac{5\pi }{12}$ = $\frac{\pi }{4}$ + $\frac{\pi }{6}$ , thus

sin($\frac{5\pi }{12}$)

= sin($\frac{\pi }{4}$ + $\frac{\pi }{6}$ )

= sin($\frac{\pi }{4}$)cos($\frac{\pi }{6}$ ) + cos($\frac{\pi }{4}$)sin($\frac{\pi }{6}$)

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

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

= $\frac{\sqrt{6}+\sqrt{2} }{4}$ → D