If sin θ = 4/5 and θ is in the second quadrant, what is the value of tan θ?
Show the answer and explanation
Correct answer
A. -4/3
Principle or equation
In the second quadrant, sine is positive, cosine is negative. Use the Pythagorean identity sin²θ + cos²θ = 1 to find cos θ, then tan θ = sin θ / cos θ.
Why this answer is correct
sin θ = 4/5, so cos²θ = 1 - (16/25) = 9/25, so cos θ = ±3/5. Since θ is in the second quadrant, cos θ = -3/5. Therefore tan θ = (4/5) / (-3/5) = -4/3.
Example
If sin θ = 3/5 and θ is in the second quadrant, then cos θ = -4/5 and tan θ = -3/4.
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