What is the general solution for -15+4cos(x)=-15-2sqrt(2) ?

The general solution for -15+4cos(x)=-15-2sqrt(2) is x=(3pi)/4+2pin,x=(5pi)/4+2pin

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-15+4cos(x)=-15-2sqrt(2)

- 15 + 4 cos (x) = - 15 - 22

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Degrees

x = 13 5^{\circ} + 36 0^{\circ} n, x = 22 5^{\circ} + 36 0^{\circ} n

Solution steps

- 15 + 4 cos (x) = - 15 - 22

Add

15

to both sides

- 15 + 4 cos (x) + 15 = - 15 - 22 + 15

Simplify

4 cos (x) = - 22

Divide both sides by

4

4 cos (x) = - 22

Divide both sides by

4

\frac{4 cos ( x )}{4} = \frac{- 2 2}{4}

Simplify

\frac{4 cos ( x )}{4} = \frac{- 2 2}{4}

Simplify

\frac{4 cos ( x )}{4} : cos (x)

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

Divide the numbers:

\frac{4}{4} = 1

= cos (x)

Simplify

\frac{- 2 2}{4} : - \frac{2}{2}

\frac{- 2 2}{4}

Apply the fraction rule:

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

= - \frac{2 2}{4}

Cancel the common factor:

2

= - \frac{2}{2}

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

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

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

General solutions for

cos (x) = - \frac{2}{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{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

tan^{2} (x) sin (x) = tan^{2} (x)

2 sin (θ) = 2, 0 \leq θ < 2 π

2 cos^{2} (t) - 3 cos (t) = - 1

cos (t) - cos (2 t) = - 0.75

2 cos (A) = - 3

What is the general solution for -15+4cos(x)=-15-2sqrt(2) ?
The general solution for -15+4cos(x)=-15-2sqrt(2) is x=(3pi)/4+2pin,x=(5pi)/4+2pin