What is the general solution for 6cos(6x)=5 ?

The general solution for 6cos(6x)=5 is x=(0.58568…)/6+(pin)/3 ,x= pi/3-(0.58568…)/6+(pin)/3

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6cos(6x)=5

6 cos (6 x) = 5

x = \frac{0.58568 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.58568 \dots}{6} + \frac{πn}{3}

Solution steps

6 cos (6 x) = 5

Divide both sides by

6

cos (6 x) = \frac{5}{6}

Apply trig inverse properties

6 x = arccos (\frac{5}{6}) + 2 πn, 6 x = 2 π - arccos (\frac{5}{6}) + 2 πn

Solve

6 x = arccos (\frac{5}{6}) + 2 πn : x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

Solve

6 x = 2 π - arccos (\frac{5}{6}) + 2 πn : x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{0.58568 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.58568 \dots}{6} + \frac{πn}{3}

4 sec (x) + 23 = sec (x)

sec (x) sin (x) = 2

sec (x) cot (x) = \frac{7}{6}

tan (x) cos (x) = 0

sin^{2} (x) - 3 sin (x) cos (x) + 2 cos^{2} (x) = 0

What is the general solution for 6cos(6x)=5 ?
The general solution for 6cos(6x)=5 is x=(0.58568…)/6+(pin)/3 ,x= pi/3-(0.58568…)/6+(pin)/3