Find the Sine Given the Point (7/25,24/25)

Problem

sin(θ)* given *(x,y)=(7/25,24/25)

Solution

1. Identify the coordinates of the given point on the Cartesian plane.

x=7/25

y=24/25

2. Recall the definition of the sine function for a point (x,y) on a circle of radius r

sin(θ)=y/r

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

r=√(,(7/25)2+(24/25)2)

r=√(,49/625+576/625)

r=√(,625/625)

r=1

4. Substitute the values of y and r into the sine formula.

sin(θ)=(24/25)/1

sin(θ)=24/25

Final Answer

sin(θ)=24/25

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