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By using trigonometric identities find the value of sin A if tan A equals a half?
Wiki User
∙ 14y ago
If tan A = 1/2, then sin A = ?
We use the Pythagorean identity 1 + cot2 A = csc2 A to find csc A, and then the reciprocal identity sin A = 1/csc A to find sin A.
tan A = 1/2 (since tan A is positive, A is in the first or the third quadrant)
cot A = 1/tan A = 1/(1/2) = 2
1 + cot2 A = csc2 A
1 + (2)2 = csc2 A
5 = csc2 A
√5 = csc A (when A is in the first quadrant)
1/√5 = sin A
√5/5 = sin A
If A is in the third quadrant, then sin A = -√5/5.
Wiki User
∙ 14y ago
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