Question

If sin theta equals 12 divided by 13 and theta is in quadrant 2 cos20 equals? and cos theta equals?

Answer 1

Answers:

• cos(2theta) = -119/169
• cos(theta) = -5/13

=====================================================

The given info is:

• sin(theta) = 12/13
• theta is in quadrant II

From that, we can use the pythagorean trig identity to find that cos(theta) = -5/13. Keep in mind that cosine is negative in quadrant II.

Now use the trig identity below to compute cos(2theta)

`\cos(2\theta) = \cos^2(\theta)-\sin^2(\theta)\\\\\cos(2\theta) = \left((-5)/(13)\right)^2-\left((12)/(13)\right)^2\\\\\cos(2\theta) = (25)/(169)-(144)/(169)\\\\\cos(2\theta) = (25-144)/(169)\\\\\cos(2\theta) = -(119)/(169)\\\\`

Other options you could use are these identities

`\cos(2\theta) = 2\cos^2(\theta)-1\\\\`

or

`\cos(2\theta) = 1-2\sin^2(\theta)\\\\`