What is the general solution for 2cos(x)= 6/7 ?

The general solution for 2cos(x)= 6/7 is x=1.12788…+2pin,x=2pi-1.12788…+2pin

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2cos(x)= 6/7

2 cos (x) = \frac{6}{7}

x = 1.12788 \dots + 2 πn, x = 2 π - 1.12788 \dots + 2 πn

Degrees

x = 64.62306 \dots^{\circ} + 36 0^{\circ} n, x = 295.37693 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 cos (x) = \frac{6}{7}

Divide both sides by

2

2 cos (x) = \frac{6}{7}

Divide both sides by

2

\frac{2 cos ( x )}{2} = \frac{\frac{6}{7}}{2}

Simplify

\frac{2 cos ( x )}{2} = \frac{\frac{6}{7}}{2}

Simplify

\frac{2 cos ( x )}{2} : cos (x)

\frac{2 cos ( x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= cos (x)

Simplify

\frac{\frac{6}{7}}{2} : \frac{3}{7}

\frac{\frac{6}{7}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{6}{7 \cdot 2}

Multiply the numbers:

7 \cdot 2 = 14

= \frac{6}{14}

Cancel the common factor:

2

= \frac{3}{7}

cos (x) = \frac{3}{7}

cos (x) = \frac{3}{7}

cos (x) = \frac{3}{7}

Apply trig inverse properties

cos (x) = \frac{3}{7}

General solutions for

cos (x) = \frac{3}{7}

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

x = arccos (\frac{3}{7}) + 2 πn, x = 2 π - arccos (\frac{3}{7}) + 2 πn

x = arccos (\frac{3}{7}) + 2 πn, x = 2 π - arccos (\frac{3}{7}) + 2 πn

Show solutions in decimal form

x = 1.12788 \dots + 2 πn, x = 2 π - 1.12788 \dots + 2 πn

tan (θ) = \frac{1}{2}, π < θ < \frac{3 π}{2}

\frac{7}{2} = 3 sin (b (\frac{π}{2})) + 2

cos (x) = \frac{2}{8}

y, x = 4 sin (2 y)

cos^{2} (x) - \frac{5}{2} cos (x) - \frac{3}{2} = 0

What is the general solution for 2cos(x)= 6/7 ?
The general solution for 2cos(x)= 6/7 is x=1.12788…+2pin,x=2pi-1.12788…+2pin