Question

Find the exact value of sin 105 degrees​

Answer 1

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

Answer 2

Answer:

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

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.

$\sin(105)=\sin(60+45)$

$\sin(60)\cos(45)+\sin(45)\cos(60)$

Plug in the values for sin(60),cos(45), sin(45),cos(60)

$\frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\frac{1}{2}$

$\frac{\sqrt{3}\sqrt{2}+\sqrt{2}}{4}$

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