Find the exact values of the six trigonometric functions of 𝜃 if 𝜃 is in standard position and P is on the terminal side.

Question

Find the exact values of the six trigonometric functions of 𝜃 if 𝜃 is in standard position and P is on the terminal side.

P(−24, −7)

Answer 1

P is in quadrant 3.

right triangle formed with horizontal leg (adjacent side) = -24, vertical leg (opposite side) = -7 and hypotenuse = sqrt((-24)^2 + (-7)^2) = 25

sin = opposite side/hypotenuse = -7/25

cos = adjacent side /hypotenuse = -24/25

tan = sin/cos = 7/24

cot = 1/tan = 24/7

csc = 1/sin = -25/7

sec = 1/cos = -25/24