Find the Exact Value sin(405)

Problem

sin(405)

Solution

1. Identify the angle as being greater than 360 which means it completes more than one full revolution around the unit circle.

2. Find the coterminal angle by subtracting 360 from 405 to bring the angle within the standard range of 0 to 360

405−360=45

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

sin(405)=sin(45)

4. Determine the exact value of sin(45) using the unit circle or a special right triangle (45−45−90.

sin(45)=√(,2)/2

Final Answer

sin(405)=√(,2)/2

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