anonymous
  • anonymous
Find the exact value of sin(105.0 degrees), without a calculator, using double-angle and/or half-angle identities.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
180-75
anonymous
  • anonymous
its just playing with numbers and getting a feel for it
anonymous
  • anonymous
= sin(180-75) = sin180cos75 - cos180sin75

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anonymous
  • anonymous
sin(180) =0 so first term disappears
anonymous
  • anonymous
and cos(180) = -1 so the second term becomes +sin(75) = sin(30+45) = sin30cos45 + cos30sin45
anonymous
  • anonymous
How do I convert that to an answer such as \[A. (\sqrt{2-\sqrt{2}})/ 2 B. (\sqrt{2-\sqrt{3}})/ 2 C. (\sqrt{2+\sqrt{3}})/ 2 D. -(\sqrt{2-\sqrt{3}})/ 2\] \[E. (\sqrt{2+\sqrt{2}})/ 2\]

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