David is told that an angle has a cosine of −3√2

Question

and is in Quadrant III. Use the Pythagorean identity sin2(θ)+cos2(θ)=1
and the quadrant to find the sine.(1 point)

Answer 1

In Quadrant III, the cosine of an angle is negative and the sine of an angle is also negative.

Using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1, we can solve for the sine:
sin^2(θ) = 1 - cos^2(θ)
sin^2(θ) = 1 - (-3√2)^2
sin^2(θ) = 1 - 18
sin^2(θ) = -17

Since the sine of an angle in Quadrant III is negative, we can conclude that the sine of the angle David is looking for is -√17.