What is the general solution for 3sin^2(t)-2sin(t)-1=0 ?

The general solution for 3sin^2(t)-2sin(t)-1=0 is t= pi/2+2pin,t=-0.33983…+2pin,t=pi+0.33983…+2pin

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3sin^2(t)-2sin(t)-1=0

3 sin^{2} (t) - 2 sin (t) - 1 = 0

t = \frac{π}{2} + 2 πn, t = - 0.33983 \dots + 2 πn, t = π + 0.33983 \dots + 2 πn

Solution steps

3 sin^{2} (t) - 2 sin (t) - 1 = 0

Solve by substitution

sin (t) = 1, sin (t) = - \frac{1}{3}

sin (t) = 1 : t = \frac{π}{2} + 2 πn

sin (t) = - \frac{1}{3} : t = arcsin (- \frac{1}{3}) + 2 πn, t = π + arcsin (\frac{1}{3}) + 2 πn

Combine all the solutions

t = \frac{π}{2} + 2 πn, t = arcsin (- \frac{1}{3}) + 2 πn, t = π + arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

t = \frac{π}{2} + 2 πn, t = - 0.33983 \dots + 2 πn, t = π + 0.33983 \dots + 2 πn

3 sin^{2} (x) + cos^{2} (x) = 2

tan (2 x) = 4

2 sin (2 x) = 1, in t er v a l (0, 36 0^{\circ})

sinh (x + 1) = 0

sin (a) = 0.6542

What is the general solution for 3sin^2(t)-2sin(t)-1=0 ?
The general solution for 3sin^2(t)-2sin(t)-1=0 is t= pi/2+2pin,t=-0.33983…+2pin,t=pi+0.33983…+2pin