What is the general solution for 2sin(2x)+5=4 ?

The general solution for 2sin(2x)+5=4 is x=(7pi)/(12)+pin,x=(11pi)/(12)+pin

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2sin(2x)+5=4

2 sin (2 x) + 5 = 4

x = \frac{7 π}{12} + πn, x = \frac{11 π}{12} + πn

Solution steps

2 sin (2 x) + 5 = 4

Move

5

to the right side

2 sin (2 x) = - 1

Divide both sides by

2

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

General solutions for

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

2 x = \frac{7 π}{6} + 2 πn, 2 x = \frac{11 π}{6} + 2 πn

Solve

2 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{12} + πn

Solve

2 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{12} + πn

x = \frac{7 π}{12} + πn, x = \frac{11 π}{12} + πn

x, sin (x) = cos (x)

sin (θ) = - \frac{3}{2}, 0 \leq θ \leq 2 π

sin (x) + cos (x) = \frac{1}{2}

cot (x) = 4

sin (x) = 0.2765

What is the general solution for 2sin(2x)+5=4 ?
The general solution for 2sin(2x)+5=4 is x=(7pi)/(12)+pin,x=(11pi)/(12)+pin