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

The general solution for 2cos(3t)-1=0 is t= pi/9+(2pin)/3 ,t=(5pi)/9+(2pin)/3

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2cos(3t)-1=0

2 cos (3 t) - 1 = 0

t = \frac{π}{9} + \frac{2 πn}{3}, t = \frac{5 π}{9} + \frac{2 πn}{3}

Solution steps

2 cos (3 t) - 1 = 0

Move

1

to the right side

2 cos (3 t) = 1

Divide both sides by

2

cos (3 t) = \frac{1}{2}

General solutions for

cos (3 t) = \frac{1}{2}

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

Solve

3 t = \frac{π}{3} + 2 πn : t = \frac{π}{9} + \frac{2 πn}{3}

Solve

3 t = \frac{5 π}{3} + 2 πn : t = \frac{5 π}{9} + \frac{2 πn}{3}

t = \frac{π}{9} + \frac{2 πn}{3}, t = \frac{5 π}{9} + \frac{2 πn}{3}

sin (x) + cos (x) - 1 = 0

tan (θ) = - 9

tan (θ) = 13

tan (θ) = 16

cos (θ) = - \frac{1}{5}

What is the general solution for 2cos(3t)-1=0 ?
The general solution for 2cos(3t)-1=0 is t= pi/9+(2pin)/3 ,t=(5pi)/9+(2pin)/3