Find the Value Using the Unit Circle sin(45 degrees )

Problem

sin(45^∘)

Solution

1. Identify the angle on the unit circle. The angle 45^∘ is located in the first quadrant.

2. Recall the coordinates (x,y) for the angle 45^∘ on the unit circle. For 45^∘ the coordinates are (√(,2)/2,√(,2)/2)

3. Apply the definition of the sine function on the unit circle. The value of sin(θ) corresponds to the ycoordinate of the point.

4. Extract the ycoordinate from the point (√(,2)/2,√(,2)/2)

Final Answer

sin(45^∘)=√(,2)/2

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