What is the general solution for 1=6cos(x) ?

The general solution for 1=6cos(x) is x=1.40334…+2pin,x=2pi-1.40334…+2pin

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1=6cos(x)

1 = 6 cos (x)

x = 1.40334 \dots + 2 πn, x = 2 π - 1.40334 \dots + 2 πn

Degrees

x = 80.40593 \dots^{\circ} + 36 0^{\circ} n, x = 279.59406 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1 = 6 cos (x)

Switch sides

6 cos (x) = 1

Divide both sides by

6

6 cos (x) = 1

Divide both sides by

6

\frac{6 cos ( x )}{6} = \frac{1}{6}

Simplify

cos (x) = \frac{1}{6}

cos (x) = \frac{1}{6}

Apply trig inverse properties

cos (x) = \frac{1}{6}

General solutions for

cos (x) = \frac{1}{6}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{1}{6}) + 2 πn, x = 2 π - arccos (\frac{1}{6}) + 2 πn

x = arccos (\frac{1}{6}) + 2 πn, x = 2 π - arccos (\frac{1}{6}) + 2 πn

Show solutions in decimal form

x = 1.40334 \dots + 2 πn, x = 2 π - 1.40334 \dots + 2 πn

x, sec (x) = 0

sin (\frac{x}{3}) = \frac{3}{2}

2 cos (θ) sin (θ) - cos (θ) = 0

- sin (x) = cos (2 x)

2 sin (2 (x - \frac{π}{3})) = - 3

What is the general solution for 1=6cos(x) ?
The general solution for 1=6cos(x) is x=1.40334…+2pin,x=2pi-1.40334…+2pin