Question

If cos theta=-3/5 in quadrant 2 what is sin theta? A:4/5 B:3/4 C:-3/4 D:-4/5

Answer 1

Answer: Choice A) 4/5

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Work Shown:

cos^2(theta) + sin^2(theta) = 1
(-3/5)^2 + sin^2(theta) = 1
9/25 + sin^2(theta) = 1
9/25 + sin^2(theta) - 9/25 = 1 - 9/25
sin^2(theta) = 1 - 9/25
sin^2(theta) = 25/25 - 9/25
sin^2(theta) = (25 - 9)/25
sin^2(theta) = 16/25
sqrt[sin^2(theta)] = sqrt[16/25]
sin(theta) = 4/5

The fact that sine is positive in quadrant 2 means that the result is positive.