What ia the value of cosθ given that (-2,9) is a point on the terminal side of θ ? A. - (9 √(85) )/(85) B. -(2 √(85) )/(85) C. (9 √(85) )/(85) D. (2 √(85) )/(85)

Question

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

A.

`- (9 √(85) )/(85)`
B.

`-(2 √(85) )/(85)`
C.

`(9 √(85) )/(85)`
D.

`(2 √(85) )/(85)`

Answer 1

Hello from MrBillDoesMath!

Answer:

Choice B, -2 sqrt(85) / 85

Discussion:

By definition,

cos(@) = length of side adjacent to angle / hypotenuse

= -2/ ( sqrt ( (-2)^2 + (9^2) ) (usin Pythag. theorem)

= -2/ sqty (4 + 81)

= -2 / (sqrt(85)

Multiply numerator and denominator by sqrt(85):

= (-2 / ( sqrt(85) ) * (sqrt(85)/sqrt(85) )

= -2 sqrt(85) / 85

which is choice B

Thank you,

MrB