Find the Sine Given the Point (7,-2)

Problem

sin(θ)* given *(7,−2)

Solution

1. Identify the coordinates of the given point (x,y) where x=7 and y=−2

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

r=√(,7+(−2)2)

r=√(,49+4)

r=√(,53)

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

sin(θ)=(−2)/√(,53)

4. Rationalize the denominator by multiplying the numerator and denominator by √(,53)

sin(θ)=(−2√(,53))/53

Final Answer

sin(θ)=−(2√(,53))/53

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