P(-15/17,-8/17) is found on the unit circle. Find sin theta and cos theta.
P(-15/17,-8/17)= P(cos theta,sin theta)
sin=-8/17
cos=-15/17
The x side, y side and radius form a right triangle with side ratio 8:15:17
cos theta is x/r = -15/17 and sin theta is -8/17
So your answer is correct
To find the values of sin theta and cos theta for the point P(-15/17,-8/17) on the unit circle, you can use the Pythagorean theorem.
1. First, find the hypotenuse of the right triangle formed by the x and y coordinates of the point P. The hypotenuse is the radius of the unit circle, which is always 1. In this case, the hypotenuse is the distance between the origin and the point P, which can be calculated using the formula:
hypotenuse = √((-15/17)^2 + (-8/17)^2)
2. Once you find the hypotenuse, you can determine sin theta and cos theta using the following formulas:
sin theta = opposite/hypotenuse = (-8/17) / hypotenuse
cos theta = adjacent/hypotenuse = (-15/17) / hypotenuse
Substitute the value of hypotenuse you found in step 1 into the formulas for sin theta and cos theta to calculate their values. In this case:
sin theta = (-8/17) / hypotenuse
cos theta = (-15/17) / hypotenuse
After applying these calculations, you will find that sin theta = -8/17 and cos theta = -15/17 for the point P(-15/17,-8/17) on the unit circle.