What is the general solution for 3sin^2(w)-4sin(w)-4=0 ?

The general solution for 3sin^2(w)-4sin(w)-4=0 is w=-0.72972…+2pin,w=pi+0.72972…+2pin

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3sin^2(w)-4sin(w)-4=0

3 sin^{2} (w) - 4 sin (w) - 4 = 0

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

Solution steps

3 sin^{2} (w) - 4 sin (w) - 4 = 0

Solve by substitution

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

sin (w) = 2 :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

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

sin (θ) = \frac{9}{10}

2 sec^{2} (x) - tan^{2} (x) = 3

tan (x) - 2 sin (x) = 0

4 sin (2 t) = 4 cos (t)

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

What is the general solution for 3sin^2(w)-4sin(w)-4=0 ?
The general solution for 3sin^2(w)-4sin(w)-4=0 is w=-0.72972…+2pin,w=pi+0.72972…+2pin