Question

Angle θ is in standard position. if sin(θ) = − 1/3, and π < θ < 3π/2 , find cos(θ).

A. -(2√2)/3
B.4/3
C.2√2/3

Answer 1

Explanation:

`sin^2({ \theta})+cos^2({ \theta})=1\\cos({ \theta})=-/+\sqrt{1-sin^2({ \theta})} \\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} \\ --- > sin({ \theta})=(1)/(3) (known)\\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} =-\sqrt{1-(-(1)/(3))} =-\sqrt{(9-1)/(9)} =-(2x^(2) )/(3)`