Find the Sine Given the Point ( square root of 6,- square root of 2)

Problem

Find *sin(θ)* given the point *(√(,6),−√(,2))

Solution

1. Identify the coordinates of the given point (x,y) where x=√(,6) and y=−√(,2)

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

r=√(,(√(,6))2+(−√(,2))2)

3. Simplify the expression under the radical to find the value of r

r=√(,6+2)

r=√(,8)

r=2√(,2)

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

sin(θ)=(−√(,2))/(2√(,2))

5. Simplify the fraction by canceling the common factor √(,2) from the numerator and the denominator.

sin(θ)=−1/2

Final Answer

sin(θ)=−1/2

Want more problems? Check here!