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(−8, −15)

sin 𝜃	=
cos 𝜃	=
tan 𝜃	=
csc 𝜃	=
sec 𝜃	=
cot 𝜃	=

Answer 1

Point P and x and y axes can be used to form a right triangle.

Point P is in third quadrant.

Length of hypotenuse = sqrt((-8)^2 + (-15)^2) = 17

-8 is length of adjacent side and -15 is length of opposite side.

sin = opp/hyp = -15/17

cos = adj/hyp = -8/17

tan = sin/cos = 15/8

cot = 1/tan = 8/15

csc = 1/sin = -17/15

sec = 1/cos = -17/8

Answer 2

It's quadrant III

8^2 + 15^2 = 64+225 = 289 = 17^2,

It's an 8-15-17 triangle, 17 is the hypotenuse

let a=adjacent side, o = opposite side

sin(theta) =-o/h= -15/17

cos(theta) =-a/h= -8/17

sec(theta) =h/a = -17/8

csc(theta) =-h/o = -17/15

tan(theta) = o/a =8/15

cot(theta) = a/o = 15/8

only tan and cot are positive in quadrant III