What is the general solution for 3sin^2(t)-7sin(t)-6=0 ?

The general solution for 3sin^2(t)-7sin(t)-6=0 is t=-0.72972…+2pin,t=pi+0.72972…+2pin

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3sin^2(t)-7sin(t)-6=0

3 sin^{2} (t) - 7 sin (t) - 6 = 0

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

Solution steps

3 sin^{2} (t) - 7 sin (t) - 6 = 0

Solve by substitution

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

sin (t) = 3 :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

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

sin (s) = - \frac{2}{2}

cos^{2} (θ) + 2 cos (θ) + 1 = 0, 0 \leq θ < 2 π

950 sin (\frac{π}{6} (7 - x)) + 1650 = 2500

sin (θ) = 12

sin (2 x - \frac{π}{6}) = - \frac{1}{2}

What is the general solution for 3sin^2(t)-7sin(t)-6=0 ?
The general solution for 3sin^2(t)-7sin(t)-6=0 is t=-0.72972…+2pin,t=pi+0.72972…+2pin