What is the general solution for sqrt(2)cos(3θ)+1=0 ?

The general solution for sqrt(2)cos(3θ)+1=0 is θ= pi/4+(2pin)/3 ,θ=(5pi}{12}+\frac{2pin)/3

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sqrt(2)cos(3θ)+1=0

2 cos (3 θ) + 1 = 0

θ = \frac{π}{4} + \frac{2 πn}{3}, θ = \frac{5 π}{12} + \frac{2 πn}{3}

Solution steps

2 cos (3 θ) + 1 = 0

Move

1

to the right side

2 cos (3 θ) = - 1

Divide both sides by

2

cos (3 θ) = - \frac{2}{2}

General solutions for

cos (3 θ) = - \frac{2}{2}

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

Solve

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

Solve

3 θ = \frac{5 π}{4} + 2 πn : θ = \frac{5 π}{12} + \frac{2 πn}{3}

θ = \frac{π}{4} + \frac{2 πn}{3}, θ = \frac{5 π}{12} + \frac{2 πn}{3}

cos (a) = - \frac{3}{5}

tan (x) = 3.5

sec (θ) = \frac{1}{sec ( θ )}

- 2 tan (θ) + 1 = 3 tan (θ) - 7

5 cos (x) + 2 = 3 cos (x)

What is the general solution for sqrt(2)cos(3θ)+1=0 ?
The general solution for sqrt(2)cos(3θ)+1=0 is θ= pi/4+(2pin)/3 ,θ=(5pi}{12}+\frac{2pin)/3