Posted by **Spy[c]** on Wednesday, September 22, 2010 at 10:23pm.

Solving Trig Functions: How Do You Solve For Sin 7.5 Using Half-Angle and Double-Angle Identities?

- trig -
**MathMate**, Wednesday, September 22, 2010 at 11:04pm
Formulas to remember:

sin(2a)=2sin(a)cos(a)

cos(2a)=cos²(a)-sin²(a)

From the second equation, replace a by a/2 and 2a by a to get

cos(a)=cos²(a/2)-sin²(a/2)

=2cos²(a/2)-1 ...(1)

=1-2sin²(a/2) ...(2)

From (1) we get

cos²(a/2)=(1/2)(1+cos(a))

From (2) we get

sin²(a/2)=(1/2)(1-cos(a))

So

sin(7.5)

=√((1/2)(1-cos(15))

=√((1/2)(1-√((1/2)(1+cos(30))))

=√((1/2)(1-√((1/2)(1+√(3)/2)))

=0.13...

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