What is the general solution for 2cos(x)= 1/2 ?

The general solution for 2cos(x)= 1/2 is x=1.31811…+2pin,x=2pi-1.31811…+2pin

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2cos(x)= 1/2

2 cos (x) = \frac{1}{2}

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

Degrees

x = 75.52248 \dots^{\circ} + 36 0^{\circ} n, x = 284.47751 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 cos (x) = \frac{1}{2}

Divide both sides by

2

2 cos (x) = \frac{1}{2}

Divide both sides by

2

\frac{2 cos ( x )}{2} = \frac{\frac{1}{2}}{2}

Simplify

\frac{2 cos ( x )}{2} = \frac{\frac{1}{2}}{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{1}{2}}{2} : \frac{1}{4}

\frac{\frac{1}{2}}{2}

Apply the fraction rule:

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

= \frac{1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

cos (x) = \frac{1}{4}

cos (x) = \frac{1}{4}

cos (x) = \frac{1}{4}

Apply trig inverse properties

cos (x) = \frac{1}{4}

General solutions for

cos (x) = \frac{1}{4}

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

x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

2 cos^{2} (x) - 1 = 1 - sin^{2} (x)

cos (x) + 0.65 = 0

sin^{2} (x) = 0.12

6 cos (x) = - 32

cos (x) = \frac{7}{12}

What is the general solution for 2cos(x)= 1/2 ?
The general solution for 2cos(x)= 1/2 is x=1.31811…+2pin,x=2pi-1.31811…+2pin