Find the Sine Given the Point (6,8)

Problem

sin(θ)* given *(6,8)

Solution

1. Identify the coordinates of the given point (x,y) where x=6 and y=8

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

r=√(,6+8)

r=√(,36+64)

r=√(,100)

r=10

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

sin(θ)=8/10

4. Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2

sin(θ)=4/5

Final Answer

sin(θ)=4/5

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