What is the general solution for 1/2 =sqrt(3/2)*cos(x) ?

The general solution for 1/2 =sqrt(3/2)*cos(x) is x=1.15026…+2pin,x=2pi-1.15026…+2pin

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1/2 =sqrt(3/2)*cos(x)

\frac{1}{2} = \frac{3}{2} \cdot cos (x)

x = 1.15026 \dots + 2 πn, x = 2 π - 1.15026 \dots + 2 πn

Solution steps

\frac{1}{2} = \frac{3}{2} cos (x)

Switch sides

\frac{3}{2} cos (x) = \frac{1}{2}

Divide both sides by

\frac{3}{2}

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

Apply trig inverse properties

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

Show solutions in decimal form

x = 1.15026 \dots + 2 πn, x = 2 π - 1.15026 \dots + 2 πn

cos (\frac{x}{2}) = - 12

4 sin (β) + 2 = 3 + 2 sin (β)

3 sin^{2} (x) = cos (x)

cos (3 x) = 0, 0 \leq x \leq 2 π

2 = csc (θ)

What is the general solution for 1/2 =sqrt(3/2)*cos(x) ?
The general solution for 1/2 =sqrt(3/2)*cos(x) is x=1.15026…+2pin,x=2pi-1.15026…+2pin