What is the general solution for 5sin^2(x)-6sin(x)cos(x)=0 ?

The general solution for 5sin^2(x)-6sin(x)cos(x)=0 is x=2pin,x=pi+2pin,x=0.87605…+pin

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5sin^2(x)-6sin(x)cos(x)=0

5 sin^{2} (x) - 6 sin (x) cos (x) = 0

x = 2 πn, x = π + 2 πn, x = 0.87605 \dots + πn

Solution steps

5 sin^{2} (x) - 6 sin (x) cos (x) = 0

Factor

5 sin^{2} (x) - 6 sin (x) cos (x) : sin (x) (5 sin (x) - 6 cos (x))

sin (x) (5 sin (x) - 6 cos (x)) = 0

Solving each part separately

sin (x) = 0 or 5 sin (x) - 6 cos (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

5 sin (x) - 6 cos (x) = 0 : x = arctan (\frac{6}{5}) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (\frac{6}{5}) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 0.87605 \dots + πn

10 sin (20 t - \frac{π}{6}) = 8

x, - cos (x) = 0

sin^{2} (x) tan^{2} (x) = tan^{2} (x) + sin^{2} (x)

θ, cot (θ) = - \frac{π}{6}

tan (x) + cos (x) = 0

What is the general solution for 5sin^2(x)-6sin(x)cos(x)=0 ?
The general solution for 5sin^2(x)-6sin(x)cos(x)=0 is x=2pin,x=pi+2pin,x=0.87605…+pin