Simplify sin(405)

Problem

sin(405)

Solution

1. Identify the angle as being greater than 360 and find its coterminal equivalent within the range [0,360)

2. Subtract 360 from the given angle to find the coterminal angle.

θ=405−360

θ=45

3. Apply the property that trigonometric functions of coterminal angles are equal.

sin(405)=sin(45)

4. Evaluate the sine of the reference angle using the unit circle or special right triangles.

sin(45)=√(,2)/2

Final Answer

sin(405)=√(,2)/2

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