SOLUTION: Please explain how to find the values of the trigonometric functions of θ from the information given? tan(θ) = 11/6 θ in quadrant III sin(θ) = cos(&#

Algebra ->  Trigonometry-basics -> SOLUTION: Please explain how to find the values of the trigonometric functions of θ from the information given? tan(θ) = 11/6 θ in quadrant III sin(θ) = cos(&#      Log On


   

Question 929334: Please explain how to find the values of the trigonometric functions of θ from the information given?
tan(θ) = 11/6
θ in quadrant III

sin(θ) =
cos(θ) =
cot(θ) =
sec(θ) =
csc(θ) =

THANKS!
Found 2 solutions by ewatrrr, Fombitz:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
tan(θ) = sin/cos = 11/6
sqrt(11^ + 6^2) = √157
quadrant III
........
sin(θ) = -11/√157
cos(θ) = -6/√157
cot(θ) = 6/11
sec(θ) = -√157/6
csc(θ) = -√157/11

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28theta%29=11%2FZ
cos%28theta%29=6%2FZ
%2811%2FZ%29%5E2%2B%286%2FZ%29%5E2=1
121%2FZ%5E2%2B36%2FZ%5E2=1
157%2FZ%5E2=1
Z%5E2=157
Z=0+%2B-+sqrt%28157%29
Since the angle is in the third quadrant, both sin and cos are negative, so Z must be negative.
Z=-sqrt%28157%29
Then,
sin%28theta%29=-%2811%2Fsqrt%28157%29%29
cos%28theta%29=-%286%2Fsqrt%28157%29%29
csc%28theta%29=-%28sqrt%28157%29%2F11%29
sec%28theta%29=-%28sqrt%28157%29%2F6%29
cot%28theta%29=6%2F11