SOLUTION: The point (-3,3) is on the terminal side of an angle (theta). find cos (theta)

Question 972184: The point (-3,3) is on the terminal side of an angle (theta). find cos (theta)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the point (-3,3) is on the terminal side of the angle.
the length of x is equal to -3.
the length of y is equal to 3.
tangent of the angle is 3/-3 = -1
angle is -45 degrees.
that would be in quadrant 4.
in quadrant 1, the angle is 45 degrees.
in quadrant 2, the angle is 180 - 45 = 135 degrees.
tan(135) is equal to -1.
sin(135) is equal to sqrt(2)/2
cos(135) is equal to -sqrt(2)/2

you can do this without finding the angle.

the terminal point is (-3,3).
the originating point os (0,0).
the length of the adjacent side is (-3-0) = -3
the length of the opposite side is (3-0) = 3
the hypotenuse is equal to sqrt(9 + 9) = sqrt(18) = sqrt(2*9) = 3*sqrt(2).

sine is equal to opposite divided by hypotenuse = 3/(3*sqrt(2) = 1/sqrt(2) = sqrt(2)/2.

cosine is equal to adjacent divided by hypotenuse = -3/3*sqrt(2) = -1/sqrt(2) = -sqrt(2)/2.

the following picture shows you what the angle looks like.

$$$

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