Find the Sine Given the Point (5,5)

Problem

Find *sin(θ)* given the point *(5,5)

Solution

1. Identify the coordinates of the given point (x,y) where x=5 and y=5

2. Calculate the distance r from the origin to the point using the Pythagorean theorem formula r=√(,x2+y2)

r=√(,5+5)

r=√(,25+25)

r=√(,50)

3. Simplify the radical expression for r

r=5√(,2)

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

sin(θ)=5/(5√(,2))

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

sin(θ)=1/√(,2)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,2)

sin(θ)=√(,2)/2

Final Answer

sin(θ)=√(,2)/2

Want more problems? Check here!