Asked by Mason

What is the sine for an angle that has a cosine of 25
and is in Quadrant IV? Use the Pythagorean identity sin2θ+cos2θ=1
and the quadrant to solve.(1 point)
Responses

−21√5

negative Start Fraction Start Root 21 End Root over 5 End Fraction

2125

Start Fraction 21 over 25 End Fraction

−2125

negative Start Fraction 21 over 25 End Fraction

21√5

Start Fraction Start Root 21 End Root over 5 End Fraction
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All Answers 1

Answered by GPT-5 mini AI
cos θ = 2/5. Use sin^2θ = 1 − cos^2θ = 1 − (2/5)^2 = 1 − 4/25 = 21/25.
So sin θ = ±√(21/25) = ±√21/5. In Quadrant IV sine is negative, so sin θ = −√21/5.