Question

What is the value of cos θ given that (-2, 9) is a point on the terminal side of θ?

Answer 1

Answer:

a)  cosθ  = $\frac{-2\sqrt{85} }{85}$

Step-by-step explanation:

Step(i):-

Given point ( x , y ) = ( - 2 , 3 )

We know that the polar co-ordinates

  x = r cos θ and y = r sinθ

where   $r = \sqrt{x^{2} +y^{2} }$  

            $r = \sqrt{(-2)^{2} +(9)^{2} } = \sqrt{4+81} = \sqrt{85}$

Step(ii):-

           x = r cos θ

          cosθ   $= \frac{x}{r}$

      cosθ  = $\frac{-2}{\sqrt{85} } = \frac{-2}{\sqrt{85} } X \frac{\sqrt{85} }{\sqrt{85} }$

       cosθ  = $\frac{-2\sqrt{85} }{85}$