Find the Sine Given the Point (-10,24)

Problem

sin(θ)* given the point *(−10,24)

Solution

1. Identify the coordinates of the given point (x,y) where x=−10 and y=24

2. Calculate the radius r using the distance formula r=√(,x2+y2)

r=√(,(−10)2+24)

r=√(,100+576)

r=√(,676)

r=26

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

sin(θ)=24/26

4. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2

sin(θ)=12/13

Final Answer

sin(θ)=12/13

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