Question

Find the exact value of sin(105.0 degrees), without a calculator, using double-angle and/or half-angle identities.

Answer 1

180-75

Answer 2

its just playing with numbers and getting a feel for it

Answer 3

= sin(180-75) = sin180cos75 - cos180sin75

Answer 4

sin(180) =0

so first term disappears

Answer 5

and cos(180) = -1

so the second term becomes +sin(75) = sin(30+45) = sin30cos45 + cos30sin45

Answer 6

How do I convert that to an answer such as

\[A. (\sqrt{2-\sqrt{2}})/ 2 B. (\sqrt{2-\sqrt{3}})/ 2 C. (\sqrt{2+\sqrt{3}})/ 2 D. -(\sqrt{2-\sqrt{3}})/ 2\] \[E. (\sqrt{2+\sqrt{2}})/ 2\]