Find the Sine Given the Point (-20,48)

Problem

sin(θ)* given the point *(−20,48)

Solution

1. Identify the coordinates of the given point (x,y) where x=−20 and y=48

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

r=√(,(−20)2+48)

r=√(,400+2304)

r=√(,2704)

r=52

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

sin(θ)=48/52

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

sin(θ)=12/13

Final Answer

sin(θ)=12/13

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