Help with double angle and half angle formulas

**NeedHelp18** · April 20th 2009, 04:22 PM

If cos(t) = -sqrt.(21)/5, sin(t) = -2/5 tan(t) = 2sqrt.(21)/21
then what are the values of:

cos (2t)

sin (t/2)

tan (2t)

**skeeter** · April 20th 2009, 05:30 PM

Originally Posted by NeedHelp18

If cos(t) = -sqrt.(21)/5, sin(t) = -2/5 tan(t) = 2sqrt.(21)/21
then what are the values of:

cos (2t)

sin (t/2)

tan (2t)

note that angle $t$ is in quadrant III.

use the given values, plug and chug in the following formulas ...

$\cos(2t) = 2\cos^2{t} - 1 = 1 - 2\sin^2{t}$

$\sin\left(\frac{t}{2}\right) = \sqrt{\frac{1 - \cos{t}}{2}}$

$\tan(2t) = \frac{2\tan{t}}{1 - \tan^2{t}}$

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