Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle.

Question

sec(𝜃) = -3/2, cot(𝜃) < 0

sin(𝜃) =

cos(𝜃) =

tan(𝜃) =

csc(𝜃) =



cot(𝜃) =

Answer 1

sec = -3/2

cos = 1/sec = -2/3

since cos is negative, angle must be in 2nd or 3rd quadrant, but since cot = cos/sin < 0, sin must be > 0 and angle must be in 2nd quadrant

cos ^2 + sin^2 = 1 sin^2 = 1 - cos^2 = 1 - (-2/3)^2 = 5/9

so sin^2 = +/- sqrt(5)/3 and since sin > 0, sin = sqrt(5)/3

csc = 1/sin = 3/sqrt(5) = 3*sqrt(5)/5

tan = sin/cos = sqrt(5)/3 / (-2/3) = -sqrt(5)/2

cot = 1/tan = 2/sqrt(5) = 2*sqrt(5)/5