Find the exact value of sin 105 degrees

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.

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

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