Find the Sine Given the Point (-4,2)

Problem

sin(θ)* given the point *(−4,2)

Solution

1. Identify the coordinates of the given point (x,y) where x=−4 and y=2

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

r=√(,(−4)2+2)

r=√(,16+4)

r=√(,20)

3. Simplify the radical expression for r

r=2√(,5)

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

sin(θ)=2/(2√(,5))

5. Simplify the fraction by canceling the common factor of 2

sin(θ)=1/√(,5)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,5)

sin(θ)=√(,5)/5

Final Answer

sin(θ)=√(,5)/5

Want more problems? Check here!