SOLUTION: Use the fundamental identities to find the value of the trigonometric function: Find sin alpha if cos alpha = 2/3 and alpha is in Quadrant IV

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Question 420138: Use the fundamental identities to find the value of the trigonometric function:
Find sin alpha if cos alpha = 2/3 and alpha is in Quadrant IV
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if alpha is in the fourth quadrant, then:

the cosine is positive.

the sine is negative.

if the cosine of alpha = 2/3, this means that the x value of alpha is 2 and the hypotenuse of alpha is 3.

this makes the angle equal to -48.1896851 degrees.

the sine of -48.1896851 degrees is equal to -.745355992

since the sine of alpha equals opposite divided by hypotenuse, and since hypotenuse equals 3, then we get:

-.745355992 = y/3

we multiply both sides of this equation by 3 to get:

y = 3 * -.745355992 = -2.236067977

our angle in the fourth quadrant has an x value of 2 and a y value of -2.236067977.

the value of the hypotenuse squared is equal to x^2 + y^2 which equals 4 + 5 which equals 9.

the square root of that gets us the hypotenuse equals 3.

a picture of your angle and the triangle we created from it is shown below:

***** picture not found *****

the first quadrant is top right.
the second quadrant is top left.
the third quadrant is bottom left.
the fourth quadrant is bottom right.

alpha is the angle of the triangle whose vertex touches the intersection of the y axis and the x axis in the center of the graph.