Calculus/Hw. Help.

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Expert: - 1/27/2009


Question
Find each of the following under the given conditions. (Enter the exact answer as a fraction. Decimal answers will not be accepted. Your answer should not contain sin, cos, or tan.)

Cos(x) = -12/13
x/2 < x < pi



Find:

sin(x/2)=
cos(x/2)=
tan(x/2)=

Answer
If one leg is 12 and the hypoteneuse is 13, the other leg it
the squareroot of (13^2 - 12^2) = squareroot(169-144) =
squareroot (25) = 5, so that's the far side.

sin(x/2) = (1 - cos(x))/2,
cos(x/2) = (1 + cos(x))/2, and
tan(x/2) = sin(x/2)/cos(x/2).

It is known that cos(x) = -12/13, so we can find sin(x/2)
and cos(x/2).  Using both of these, tan(x/2) can be found.  

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