## anonymous 5 years ago Find the exact value of sin(105.0 degrees), without a calculator, using double-angle and/or half-angle identities.

1. anonymous

180-75

2. anonymous

its just playing with numbers and getting a feel for it

3. anonymous

= sin(180-75) = sin180cos75 - cos180sin75

4. anonymous

sin(180) =0 so first term disappears

5. anonymous

and cos(180) = -1 so the second term becomes +sin(75) = sin(30+45) = sin30cos45 + cos30sin45

6. anonymous

How do I convert that to an answer such as $A. (\sqrt{2-\sqrt{2}})/ 2 B. (\sqrt{2-\sqrt{3}})/ 2 C. (\sqrt{2+\sqrt{3}})/ 2 D. -(\sqrt{2-\sqrt{3}})/ 2$ $E. (\sqrt{2+\sqrt{2}})/ 2$