David is told that an angle has a cosine of −3√2
and is in Quadrant III. Use the Pythagorean identity sin2(θ)+cos2(θ)=1
and the quadrant to find the sine.(1 point)
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.