Question

How to find the value of sin 10?

Answer 1

use formula
sin3A=3sinA-4sin^3A
let A=10 degree
sin(10 x 3)=3sin10 -4sin^3(10)
sin30=3sin10-4sin^3 (10)
1/2=3sin10-3sin^3 (10)
1=6sin10-6sin^3 (10)
hence equation ,
6sin^3 (10)-6sin10+1=0 give sin10 value
but we have don't ideas factorize about this equation. we only find sin10 approx
by calculus concept of maxima and minima but this is advance math .you will study conceptually in class 12th

Answer 2

Answer:0.1736

Step-by-step explanation:

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