If tanθ = 5/12 and θ is in Quadrant III, what is the value of sinθ?
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Correct answer: B
Explanation
Given:
tanθ = 5/12
θ is in quadrant III
By the formula:
tanθ = sinθ / cosθ
sin²θ + cos²θ = 1
tanθ = 5/12
Let
sinθ = 5k
cosθ = 12k
sin²θ + cos²θ = 1
(5k)² + (12k)² = 1
25k² + 144k² = 1
169k² = 1
k = 1/13
sinθ = 5k = 5/13
sinθ is negative in quadrant III
sinθ = −5/13