Find the Exact Value sin(45 degrees )

Problem

sin(45)

Solution

1. Identify the angle on the unit circle. The angle 45 is a standard angle in the first quadrant.

2. Recall the coordinates of the terminal point for 45 on the unit circle. For an angle of 45 (or π/4 radians), the coordinates are (√(,2)/2,√(,2)/2)

3. Apply the definition of the sine function. On the unit circle, sin(θ) is equal to the ycoordinate of the terminal point.

4. Determine the value by selecting the ycoordinate from the identified point.

Final Answer

sin(45)=√(,2)/2

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