Question

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

Answer 1

a) cosθ =
`(-2√(85) )/(85)`

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) } = √(4+81) = √(85)`

Step(ii):-

x = r cos θ

cosθ
`= (x)/(r)`

cosθ =
`(-2)/(√(85) ) = (-2)/(√(85) ) X (√(85) )/(√(85) )`

cosθ =
`(-2√(85) )/(85)`