What is the general solution for -3=2sqrt(3)cos(x) ?

The general solution for -3=2sqrt(3)cos(x) is x=(5pi)/6+2pin,x=(7pi)/6+2pin

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-3=2sqrt(3)cos(x)

- 3 = 23 cos (x)

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Degrees

x = 15 0^{\circ} + 36 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n

Solution steps

- 3 = 23 cos (x)

Switch sides

23 cos (x) = - 3

Divide both sides by

23

23 cos (x) = - 3

Divide both sides by

23

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

Simplify

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

Simplify

\frac{2 3 cos ( x )}{2 3} : cos (x)

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

Divide the numbers:

\frac{2}{2} = 1

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

Cancel the common factor:

3

= cos (x)

Simplify

\frac{- 3}{2 3} : - \frac{3}{2}

\frac{- 3}{2 3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3}{2 3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{3}{2 \cdot 3 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= \frac{3 ^{1 - \frac{1}{2}}}{2}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{3 ^{\frac{1}{2}}}{2}

Apply radical rule:

3^{\frac{1}{2}} = 3

= - \frac{3}{2}

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

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

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

General solutions for

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

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x, sin (x) = a - 2 \cdot q \cdot cos (2 x)

cos (2 x) - 3 sin (- x) + 2 = 0

0 = - sin (8 x) + sin (6 x)

3 tan (x) sin (x) - 3 sin (x) = 0

cot^{4} (x) - 3 cot^{2} (x) + 1 = 0

What is the general solution for -3=2sqrt(3)cos(x) ?
The general solution for -3=2sqrt(3)cos(x) is x=(5pi)/6+2pin,x=(7pi)/6+2pin