What is the general solution for 3sin^2(x)-7sin(x)=6 ?

The general solution for 3sin^2(x)-7sin(x)=6 is x=-0.72972…+2pin,x=pi+0.72972…+2pin

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3sin^2(x)-7sin(x)=6

3 sin^{2} (x) - 7 sin (x) = 6

x = - 0.72972 \dots + 2 πn, x = π + 0.72972 \dots + 2 πn

Solution steps

3 sin^{2} (x) - 7 sin (x) = 6

Solve by substitution

sin (x) = 3, sin (x) = - \frac{2}{3}

sin (x) = 3 :

No Solution

sin (x) = - \frac{2}{3} : x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

Combine all the solutions

x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

x = - 0.72972 \dots + 2 πn, x = π + 0.72972 \dots + 2 πn

2 sin (x) (cos (x) - sin (x)) + (cos (x) - sin (x)) = 0

2 cos^{2} (x) - sin^{2} (x) + 1 = 0

- 6 sin (t) + 6 cos (2 t) = 0

cos^{2} (x) = 4

- 2 tan (θ) - sec (θ) = 0

What is the general solution for 3sin^2(x)-7sin(x)=6 ?
The general solution for 3sin^2(x)-7sin(x)=6 is x=-0.72972…+2pin,x=pi+0.72972…+2pin