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

Problem

sin(θ)* given *(x,y)=(−√(,3)/2,−1/2)

Solution

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

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

r=√(,(−√(,3)/2)2+(−1/2)2)

r=√(,3/4+1/4)

r=√(,1)=1

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

sin(θ)=(−1/2)/1

4. Simplify the expression to find the final value of the sine.

sin(θ)=−1/2

Final Answer

sin(θ)=−1/2

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