Find the Exact Value sin(10)

Problem

sin(10^∘)

Solution

1. Identify the given expression as the sine of an angle measured in degrees, sin(10^∘)

2. Determine if the angle is a standard reference angle. The angle 10^∘ is not one of the common angles (like 0^∘,30^∘,45^∘,60^∘,90^∘ found on the unit circle.

3. Express the value using the Taylor series expansion or radical forms if required. While sin(10^∘) can be expressed using complex numbers or nested radicals via the triple-angle formula sin(3*θ)=3*sin(θ)−4*sin^3(θ) these forms are not simpler than the trigonometric expression itself.

4. Conclude that the exact value is most commonly represented in its trigonometric form unless a specific radical approximation or infinite series is requested.

Final Answer

sin(10^∘)=sin(10^∘)

Want more problems? Check here!