Find the Sine Given the Point (3,-2)

Problem

sin(θ)* given *(3,−2)

Solution

1. Identify the coordinates of the given point (x,y) where x=3 and y=−2

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

r=√(,3+(−2)2)

r=√(,9+4)

r=√(,13)

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

sin(θ)=(−2)/√(,13)

4. Rationalize the denominator by multiplying the numerator and denominator by √(,13)

sin(θ)=(−2√(,13))/13

Final Answer

sin(θ)=−(2√(,13))/13

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