What is the general solution for 4sin(4θ-pi/3)+3=5 ?

The general solution for 4sin(4θ-pi/3)+3=5 is θ=(pin)/2+pi/8 ,θ=(pin)/2+(7pi)/(24)

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4sin(4θ-pi/3)+3=5

4 sin (4 θ - \frac{π}{3}) + 3 = 5

θ = \frac{πn}{2} + \frac{π}{8}, θ = \frac{πn}{2} + \frac{7 π}{24}

Solution steps

4 sin (4 θ - \frac{π}{3}) + 3 = 5

Move

3

to the right side

4 sin (4 θ - \frac{π}{3}) = 2

Divide both sides by

4

sin (4 θ - \frac{π}{3}) = \frac{1}{2}

General solutions for

sin (4 θ - \frac{π}{3}) = \frac{1}{2}

4 θ - \frac{π}{3} = \frac{π}{6} + 2 πn, 4 θ - \frac{π}{3} = \frac{5 π}{6} + 2 πn

Solve

4 θ - \frac{π}{3} = \frac{π}{6} + 2 πn : θ = \frac{πn}{2} + \frac{π}{8}

Solve

4 θ - \frac{π}{3} = \frac{5 π}{6} + 2 πn : θ = \frac{πn}{2} + \frac{7 π}{24}

θ = \frac{πn}{2} + \frac{π}{8}, θ = \frac{πn}{2} + \frac{7 π}{24}

2 tan (x) - 3 = 0

- 2 cos (2 x - \frac{π}{3}) = 2 sin (2 x - \frac{π}{6})

tan (x) = 5 sin (\frac{π}{4}) sin (\frac{3 π}{4})

cot (θ) = - \frac{12}{5}

2 - 23 tan (x + \frac{π}{3}) = 0

What is the general solution for 4sin(4θ-pi/3)+3=5 ?
The general solution for 4sin(4θ-pi/3)+3=5 is θ=(pin)/2+pi/8 ,θ=(pin)/2+(7pi)/(24)