Find the Sine Given the Point (-3,-5)

Problem

sin(θ)* given *(x,y)=(−3,−5)

Solution

1. Identify the coordinates of the given point as x=−3 and y=−5

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

r=√(,(−3)2+(−5)2)

r=√(,9+25)

r=√(,34)

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

sin(θ)=(−5)/√(,34)

4. Rationalize the denominator by multiplying the numerator and denominator by √(,34)

sin(θ)=(−5√(,34))/34

Final Answer

sin(θ)=−(5√(,34))/34

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