What is the general solution for 3sin^2(x)-10sin(x)-8=0 ?

The general solution for 3sin^2(x)-10sin(x)-8=0 is x=-0.72972…+2pin,x=pi+0.72972…+2pin

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3sin^2(x)-10sin(x)-8=0

3 sin^{2} (x) - 10 sin (x) - 8 = 0

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

Solution steps

3 sin^{2} (x) - 10 sin (x) - 8 = 0

Solve by substitution

sin (x) = 4, sin (x) = - \frac{2}{3}

sin (x) = 4 :

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 \cdot 9.8 \cdot L (1 - cos (θ)) = 0.018

cos (7 x) = sin (4 x + 2)

12 cos (β) - 5 sin (β) = 4.7

cos (x) = \frac{8}{3}

arctan (θ) = \frac{6}{8}

What is the general solution for 3sin^2(x)-10sin(x)-8=0 ?
The general solution for 3sin^2(x)-10sin(x)-8=0 is x=-0.72972…+2pin,x=pi+0.72972…+2pin