Posted by stacey graham on Friday, March 26, 2010 at 12:27am.
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
Change the third sentence to:
(Imagine a 7,24,25 right triangle)
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