Find the Exact Value sin(45)

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 point on the unit circle corresponding to 45^∘ For an angle θ the coordinates are (cos(θ),sin(θ))

3. Apply the formula for the sine of 45^∘ In a 45^∘−45^∘−90^∘ triangle with a hypotenuse of 1 the legs are both √(,2)/2

4. Determine the value. Since sin(θ) represents the y-coordinate, sin(45^∘)=√(,2)/2

Final Answer

sin(45^∘)=√(,2)/2

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