Question

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

Start Fraction Start Root 21 End Root over 5 End Fraction

−21√5

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

2125

Start Fraction 21 over 25 End Fraction

−2125

Answer 1

Assuming cos θ = 2/5: use sin^2θ = 1 − cos^2θ = 1 − (2/5)^2 = 1 − 4/25 = 21/25.
So sin θ = ±√(21)/5. In Quadrant IV sine is negative, so sin θ = −√21 / 5.