Jacques is told that an angle has a cosine of 5√4
and is in Quadrant IV. Use the Pythagorean identity sin2(θ)+cos2(θ)=1
and the quadrant to find the sine.(1 point)
Since the angle is in Quadrant IV, both the sine and cosine are negative.
Using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1, we can work backwards to find the sine:
sin^2(θ) + (5√4)^2 = 1
sin^2(θ) + 100 = 1
sin^2(θ) = 1 - 100
sin^2(θ) = -99
Since the sine is negative in Quadrant IV, we take the negative square root of -99:
sin(θ) = -√99 = -3√11
Therefore, the sine of the angle is -3√11.