SOLUTION: Find the exact value of each of the remaining trigonometric functions of &#952;. cos &#952;=-1/3 , sin &#952; < 0 sin &#952; = _______ tan &#952; = _______ csc &#952; = _______

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of each of the remaining trigonometric functions of &#952;. cos &#952;=-1/3 , sin &#952; < 0 sin &#952; = _______ tan &#952; = _______ csc &#952; = _______      Log On


   



Question 920151: Find the exact value of each of the remaining trigonometric functions of θ.
cos θ=-1/3 , sin θ < 0
sin θ = _______
tan θ = _______
csc θ = _______
sec θ = _______
cot θ = _______

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of each of the remaining trigonometric functions of θ.
cos θ=-1/3 , sin θ < 0
sin θ = -√8/3
tan θ = √8
csc θ = -3/√8=-3√8/8
sec θ = -3
cot θ = 1/√8=√8/8
***
Reference angle in quadrant III in which cos<0, sin<0
Identity: sin^2θ+cos2θ=1
sinθ=-√(1-cos^2θ)=-√(1-1/9)=-√(8/9)=-√8/3