What is sin 10 equal to? How can I find the value?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Use the relation sin 3x = 3*sin x - 4(sin x)^3

=> sin 30 = 3*sin 10 - 4*(sin 10)^3

sin 30 = 1/2 and let sin 10 = t

=> 1/2 = 3t - 4t^3

=> 8t^3 - 6t + 1 = 0

Solve for t in the cubic equation we have arrived at.

There are 3 roots of the equation, one is negative, one is greater than 0.5 and the third is 0.1736. As sin 10 < sin 30 and is positive, we can eliminate two of the roots and keep 0.1736

The value of sin 10 = 0.1736

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