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

Problem

Find *sin(θ)* given the point *(2√(,3),−2)

Solution

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

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

r=√(,(2√(,3))2+(−2)2)

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

r=√(,4*(3)+4)

r=√(,12+4)

r=√(,16)

r=4

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

sin(θ)=(−2)/4

5. Simplify the resulting fraction to its lowest terms.

sin(θ)=−1/2

Final Answer

sin(θ)=−1/2

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