If sin θ = 5/13 and θ is in the second quadrant, what is the value of cos θ?
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Correct answer
B. -12/13
Principle or equation
In the second quadrant, sine is positive and cosine is negative. Use the Pythagorean identity sin^2 θ + cos^2 θ = 1.
Why this answer is correct
Given sin θ = 5/13, we have (5/13)^2 + cos^2 θ = 1, so cos^2 θ = 1 - 25/169 = 144/169. Thus cos θ = ±12/13. Since θ is in the second quadrant, cos θ is negative, so cos θ = -12/13.
Example
If sin θ = 3/5 and θ is in the second quadrant, then cos θ = -4/5 because cos^2 θ = 1 - 9/25 = 16/25 and cosine is negative in quadrant II.
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