Find the Sine Given the Point (-8,15)

Problem

sin(θ)* given *(x,y)=(−8,15)

Solution

1. Identify the coordinates of the given point on the terminal side of the angle θ where x=−8 and y=15

2. Calculate the distance r from the origin to the point using the Pythagorean theorem formula r=√(,x2+y2)

r=√(,(−8)2+15)

r=√(,64+225)

r=√(,289)

r=17

3. Apply the formula for the sine of an angle in standard position, which is defined as sin(θ)=y/r

sin(θ)=15/17

Final Answer

sin(θ)=15/17

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