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)

## Answer this Question

## Related Questions

- Math - sin theta = 8/17 and theta is in the second quadrant. Find sin(2theta),...
- math - There are no typos and no work b/c I don't know how to do them. Thanks. 1...
- Math - 1)Find cos theta if sin theta=3/5 and 90 degrees<theta<180 degrees...
- trig - Write each identity expression in terms of:1. cos theta= a. sin^2theta...
- Algebra II - Which of the following expressions are not equal to 1? A) sin^2 ...
- Calculus - I wanted to confirm that I solved these problems correctly (we had to...
- trig - given that cos(theta)= (3/5) and sin (theta)<0, find sin(2 theta) cos...
- Math - sin theta = 8/17 and theta is in the second quadrant. Find sin(2theta),...
- trig - given that 1/2pi<theta<pi and sin theta=1/5, use appropriate ...
- Math - There are no typos and no work b/c I don't know how to do them. Thanks. 1...

More Related Questions