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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