Find the Sine Given the Point

Problem

sin(θ)* given *(x,y)=(√(,2)/2,√(,2)/2)

Solution

1. Identify the coordinates of the given point on the Cartesian plane.

x=√(,2)/2

y=√(,2)/2

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

r=√(,(√(,2)/2)2+(√(,2)/2)2)

r=√(,2/4+2/4)

r=√(,1)=1

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

sin(θ)=√(,2)/2/1

4. Simplify the expression to find the final value.

sin(θ)=√(,2)/2

Final Answer

sin(θ)=√(,2)/2

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