Question

Use a sum identity, and the fact that 105°=60°+45°, to fine the exact value of sin 105°.

Answer 1

\[\sin(\alpha +\beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)\]

Answer 2

yeah thats what we were using, how do i incorporate the numbers into there though?

Answer 3

\[\sin(45 +60)=\sin(45)\cos(60)+\sin(60)\cos(45)\]

Answer 4

awesome, i can simplify that on the right, thanks!

Answer 5

all the numbers on the right hand side should be well known\[\sin(45)=\cos(45)=\frac{\sqrt{2}}{2}\]
\[\sin(60)=\frac{\sqrt{3}}{2}, \cos(60)=\frac{1}{2}\]