Posted by **stacey graham** on Friday, March 26, 2010 at 12:27am.

tan(theta)=(7/24), sin(theta)<0

find cos(2theta)

- trig -
**drwls**, Friday, March 26, 2010 at 8:06am
If tan is positive and sin is negative, theta is in the third quadrant. From Pythagorean considerations, sin theta = -7/25 and cos theta = -24/25. (Imagine a 7,25,25 right triangle)

Use the double angle formula for

cos(2 theta)

= cos^2(theta) - sin^2(theta)

= (24^2-7^2)/25^2 = 527/625

2theta will be in the first quadrant, 32.5 degrees

Check: theta = 180 + 16.26 = 196.26 deg

2 theta = 392.50 => 32.5 degrees

- trig (correction) -
**drwls**, Friday, March 26, 2010 at 8:38am
Change the third sentence to:

(Imagine a 7,24,25 right triangle)

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