If sin θ = 12/13 and θ is in the second quadrant, what is the value of tan θ?
Show the answer and explanation
Correct answer
A. -12/5
Principle or equation
In the second quadrant, sine is positive, cosine is negative, and tangent is negative. Use the Pythagorean identity sin^2 θ + cos^2 θ = 1 to find cos θ, then tan θ = sin θ / cos θ.
Why this answer is correct
Given sin θ = 12/13, cos^2 θ = 1 - (12/13)^2 = 1 - 144/169 = 25/169, so cos θ = ±5/13. Since θ is in quadrant II, cos θ = -5/13. Then tan θ = (12/13) / (-5/13) = -12/5.
Example
If sin θ = 3/5 in quadrant II, then cos θ = -4/5 and tan θ = -3/4.
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