What is the general solution for 5cos(6x)+6=9 ?

The general solution for 5cos(6x)+6=9 is x=(0.92729…)/6+(pin)/3 ,x= pi/3-(0.92729…)/6+(pin)/3

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5cos(6x)+6=9

5 cos (6 x) + 6 = 9

x = \frac{0.92729 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{6} + \frac{πn}{3}

Solution steps

5 cos (6 x) + 6 = 9

Move

6

to the right side

5 cos (6 x) = 3

Divide both sides by

5

cos (6 x) = \frac{3}{5}

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = \frac{0.92729 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{6} + \frac{πn}{3}

sin (- \frac{5 π}{12})

4 sin (2 x) = 4 cos (x)

2 sin (x) - 3 cos (x) = 2

sec (0)

sin (33 0^{\circ})

What is the general solution for 5cos(6x)+6=9 ?
The general solution for 5cos(6x)+6=9 is x=(0.92729…)/6+(pin)/3 ,x= pi/3-(0.92729…)/6+(pin)/3