Find the Sine Given the Point (1/2,( square root of 3)/2)

Problem

sin(θ)* given *(x,y)=(1/2,√(,3)/2)

Solution

1. Identify the coordinates of the given point on the Cartesian plane, where x=1/2 and y=√(,3)/2

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

r=√(,(1/2)2+(√(,3)/2)2)

3. Simplify the expression under the square root to find the value of r

r=√(,1/4+3/4)

r=√(,1)

r=1

4. Apply the formula for the sine function in terms of coordinates, which is sin(θ)=y/r

sin(θ)=√(,3)/2/1

5. Simplify the final ratio to determine the value of the sine.

sin(θ)=√(,3)/2

Final Answer

sin(θ)=√(,3)/2

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