Find the Exact Value sin(20)

Problem

sin(20)

Solution

1. Identify the expression as the sine of 20 degrees, which is not a standard angle with a simple radical form like 30 or 45

2. Apply the triple angle formula for sine, sin(3*θ)=3*sin(θ)−4*sin3(θ) where θ=20

3. Substitute the known value sin(3⋅20)=sin(60)=√(,3)/2 into the formula.

4. Set up the cubic equation 4*x3−3*x+√(,3)/2=0 where x=sin(20)

5. Recognize that the exact value of sin(20) is typically expressed in terms of complex numbers or roots of this cubic equation using Cardano's method, as it cannot be simplified into basic square roots.

Final Answer

sin(20)=sin(20)

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