Answer:
[tex]\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]
Step-by-step explanation:
I'm going to write 105 as a sum of numbers on the unit circle.
If I do that, I must use the sum identity for sine.
[tex]\sin(105)=\sin(60+45)[/tex]
[tex]\sin(60)\cos(45)+\sin(45)\cos(60)[/tex]
Plug in the values for sin(60),cos(45), sin(45),cos(60)
[tex]\frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\frac{1}{2}[/tex]
[tex]\frac{\sqrt{3}\sqrt{2}+\sqrt{2}}{4}[/tex]
[tex]\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]
Answer:
Step-by-step explanation:
Note that 105 = 45 + 60. Therefore,
sin 105 = sin (45 + 60).
The relevant sum formula is
sin (a + b) = sin a cos b + cos a sin b
Therefore,
sin 105 = sin (45 + 60) = sin 45 cos 60 + cos 45 sin 60, or
= (1 / √2)(1 / 2) + (1 / √2)(√3 / 2)
1 + √3
= -------------
2√2
