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

The general solution for 6cos(x)=5 is x=0.58568…+2pin,x=2pi-0.58568…+2pin

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6cos(x)=5

6 cos (x) = 5

x = 0.58568 \dots + 2 πn, x = 2 π - 0.58568 \dots + 2 πn

Degrees

x = 33.55730 \dots^{\circ} + 36 0^{\circ} n, x = 326.44269 \dots^{\circ} + 36 0^{\circ} n

Solution steps

6 cos (x) = 5

Divide both sides by

6

6 cos (x) = 5

Divide both sides by

6

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Show solutions in decimal form

x = 0.58568 \dots + 2 πn, x = 2 π - 0.58568 \dots + 2 πn

6 cos (2 x) = 6 cos^{2} (x) - 5

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

tan (x) = 1, - 2 π \leq x \leq 2 π

(- 4 cos (x) - 6 sin (x))^{2} - 20 sin^{2} (x) = 16

arccos (x) = arcsin (\frac{1}{4}) + arcsin (\frac{7}{8})

What is the general solution for 6cos(x)=5 ?
The general solution for 6cos(x)=5 is x=0.58568…+2pin,x=2pi-0.58568…+2pin