SOLUTION: 2. The angle θ has the point (–2, 9) on its terminal side. What is the exact value of each of the following? (a) sin (theta) (b) cos (Theta) (c) tan (theta)

Algebra ->  Trigonometry-basics -> SOLUTION: 2. The angle θ has the point (–2, 9) on its terminal side. What is the exact value of each of the following? (a) sin (theta) (b) cos (Theta) (c) tan (theta)       Log On


   

Question 1021389: 2. The angle θ has the point (–2, 9) on its terminal side. What is the exact value of each of the following?
(a) sin (theta)
(b) cos (Theta)
(c) tan (theta)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the point is at (-2,9).
this means the angle is in the second quadrant.
the adjacent side to the angle is -2.
the opposite side to the angle is 9.
the hypotenuse of the right triangle formed is sqrt((-2)^2 + 9^2).
this is equal to sqrt(4+81) = sqrt(85)

you have:
adjacent side is -2.
opposite side is 9.
hypotenuse is sqrt(85).

the angle is theta.

you have:

sin(theta) = opp/hyp = 9/sqrt(85).
cos(theta) = adj/hyp = -2/sqrt(85).
tan(theta = opp/adj = 9/-2.