Find the Value Using the Unit Circle sin(45)

Problem

sin(45^∘)

Solution

1. Identify the angle on the unit circle. The angle 45^∘ is located in the first quadrant, exactly halfway between the xaxis and the yaxis.

2. Recall the coordinates (x,y) for the angle 45^∘ on the unit circle. For an angle θ=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. Determine the value by selecting the ycoordinate from the identified point.

Final Answer

sin(45^∘)=√(,2)/2

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