What is the general solution for -2(cos(x)-3)=7 ?

The general solution for -2(cos(x)-3)=7 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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-2(cos(x)-3)=7

- 2 (cos (x) - 3) = 7

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Degrees

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

- 2 (cos (x) - 3) = 7

Divide both sides by

- 2

- 2 (cos (x) - 3) = 7

Divide both sides by

- 2

\frac{- 2 ( cos ( x ) - 3 )}{- 2} = \frac{7}{- 2}

Simplify

cos (x) - 3 = - \frac{7}{2}

cos (x) - 3 = - \frac{7}{2}

Move

3

to the right side

cos (x) - 3 = - \frac{7}{2}

Add

3

to both sides

cos (x) - 3 + 3 = - \frac{7}{2} + 3

Simplify

cos (x) - 3 + 3 = - \frac{7}{2} + 3

Simplify

cos (x) - 3 + 3 : cos (x)

cos (x) - 3 + 3

Add similar elements:

- 3 + 3 = 0

= cos (x)

Simplify

- \frac{7}{2} + 3 : - \frac{1}{2}

- \frac{7}{2} + 3

Convert element to fraction:

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

= \frac{3 \cdot 2}{2} - \frac{7}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{3 \cdot 2 - 7}{2}

3 \cdot 2 - 7 = - 1

3 \cdot 2 - 7

Multiply the numbers:

3 \cdot 2 = 6

= 6 - 7

Subtract the numbers:

6 - 7 = - 1

= - 1

= \frac{- 1}{2}

Apply the fraction rule:

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

= - \frac{1}{2}

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

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

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

General solutions for

cos (x) = - \frac{1}{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{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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

cos (9 x) - cos (3 x) = sin (6 x)

1 - cos^{2} (θ) + 3 = 2 sin (θ) + 3

sin (4 θ) = sin (2 θ)

y, x sin (y) = x

What is the general solution for -2(cos(x)-3)=7 ?
The general solution for -2(cos(x)-3)=7 is x=(2pi)/3+2pin,x=(4pi)/3+2pin