What is the general solution for 4+4cos(x)=-6cos(x) ?

The general solution for 4+4cos(x)=-6cos(x) is x=1.98231…+2pin,x=-1.98231…+2pin

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Popular >

4+4cos(x)=-6cos(x)

Solution

4 + 4 cos (x) = - 6 cos (x)

Solution

x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

Degrees

x = 113.57817 \dots^{\circ} + 36 0^{\circ} n, x = - 113.57817 \dots^{\circ} + 36 0^{\circ} n

Solution steps

4 + 4 cos (x) = - 6 cos (x)

Solve by substitution

4 + 4 cos (x) = - 6 cos (x)

Let:

cos (x) = u

4 + 4 u = - 6 u

4 + 4 u = - 6 u : u = - \frac{2}{5}

4 + 4 u = - 6 u

Move

4

to the right side

4 + 4 u = - 6 u

Subtract

4

from both sides

4 + 4 u - 4 = - 6 u - 4

Simplify

4 u = - 6 u - 4

4 u = - 6 u - 4

Move

6 u

to the left side

4 u = - 6 u - 4

Add

6 u

to both sides

4 u + 6 u = - 6 u - 4 + 6 u

Simplify

10 u = - 4

10 u = - 4

Divide both sides by

10

10 u = - 4

Divide both sides by

10

\frac{10 u}{10} = \frac{- 4}{10}

Simplify

\frac{10 u}{10} = \frac{- 4}{10}

Simplify

\frac{10 u}{10} : u

\frac{10 u}{10}

Divide the numbers:

\frac{10}{10} = 1

= u

Simplify

\frac{- 4}{10} : - \frac{2}{5}

\frac{- 4}{10}

Apply the fraction rule:

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

= - \frac{4}{10}

Cancel the common factor:

2

= - \frac{2}{5}

u = - \frac{2}{5}

u = - \frac{2}{5}

u = - \frac{2}{5}

Substitute back

u = cos (x)

cos (x) = - \frac{2}{5}

cos (x) = - \frac{2}{5}

cos (x) = - \frac{2}{5} : x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

cos (x) = - \frac{2}{5}

Apply trig inverse properties

cos (x) = - \frac{2}{5}

General solutions for

cos (x) = - \frac{2}{5}

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

x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

Combine all the solutions

x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

Show solutions in decimal form

x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

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sin (A) = \frac{4}{5}

3tan^2(x)-1=0,0<= x<= 2pi

3 tan^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

sin(2x)=4cos(x)

sin (2 x) = 4 cos (x)

sqrt(3)tan(2x)-1=0

3 tan (2 x) - 1 = 0

Frequently Asked Questions (FAQ)

What is the general solution for 4+4cos(x)=-6cos(x) ?
The general solution for 4+4cos(x)=-6cos(x) is x=1.98231…+2pin,x=-1.98231…+2pin