Find the Exact Value sin(87)

Problem

sin(87)

Solution

1. Identify the expression as the sine of an angle measured in degrees, sin(87)

2. Recognize that 87 is not a standard reference angle (like 30 45 or 60.

3. Apply the sum formula for sine, sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B) by breaking 87 into the sum of 45 and 42

4. Determine that 42 is also not a standard angle, meaning the exact value must be expressed using radicals or the original trigonometric form if no further simplification into standard constants is possible.

5. Evaluate using the half-angle or sum/difference identities if specific radical forms are required, but for sin(87) the most common exact form involves nested radicals derived from sin(3) or cos(3)

6. State the exact value using the identity sin(87)=cos(3)

7. Expand cos(3) using the difference formula cos(18−15) or similar combinations of standard values (72,75,e*t*c. to reach the radical expression.

Final Answer

sin(87)=√(,2)/8*(√(,3)+1)√(,5+√(,5))+(√(,6)−√(,2))/16*(√(,5)−1)

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