Find the Sine Given the Point (1,3)

Problem

Find *sin(θ)* given the point *(1,3)

Solution

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

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

r=√(,1+3)

r=√(,1+9)

r=√(,10)

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

sin(θ)=3/√(,10)

4. Rationalize the denominator by multiplying the numerator and denominator by √(,10)

sin(θ)=(3√(,10))/10

Final Answer

sin(θ)=(3√(,10))/10

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