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)
Using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1, we can solve for sin(θ). We are given that cos(θ) = 5√/4.
sin^2(θ) + (5√/4)^2 = 1
sin^2(θ) + 25/4 = 1
sin^2(θ) = 1 - 25/4
sin^2(θ) = 4/4 - 25/4
sin^2(θ) = -21/4
Since sin(θ) must be positive according to the given quadrant (Quadrant IV), we can take the positive square root of -21/4:
sin(θ) = √(-21/4)
sin(θ) = √(21/4) * i, where i is the imaginary unit
Therefore, the sine of the angle is √(21/4) * i.