Question

use a half-angle formula to find the exact value of each expression
sin 105

Answer 1

@aum

Answer 2

105 = 90 + 15
sin(105) = sin(90+15) = sin(90)cos(15) + cos(90)sin(15) =
1*cos(15) + 0*sin(15) = cos(15).

Answer 3

wait wouldnt it be 105*2

Answer 4

\[
\cos^2(\frac a2) = \frac 12\{1+\cos(a) \}
\]

Answer 5

I am splitting 105 degrees into two parts: 90 degrees + 15 degrees.
90 degrees is a standard angle for which the sine and cosine are known values.
So I use the sin(A+B) formula first: sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
with A = 90 and B = 15 degrees.

Answer 6

In my first reply I showed that sin(105) = cos(15).
Now we use the half angle formula (in my second reply) and find cos(15). Set a = 30 in the half angle formula and find cos(15) and that will be the same as sin(105).

Answer 7

okay go on i get it

Answer 8

what should i do next

Answer 9

same thing we did for sin(15) in the previous problem.
set a = 30 in the half angle formula above and find cos(15).

Answer 10

okay thank you

Answer 11

you are welcome.

Answer 12

one last one?