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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