What is the general solution for -cos(a)-11=2cos(a)-9 ?

The general solution for -cos(a)-11=2cos(a)-9 is a=2.30052…+2pin,a=-2.30052…+2pin

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-cos(a)-11=2cos(a)-9

- cos (a) - 11 = 2 cos (a) - 9

a = 2.30052 \dots + 2 πn, a = - 2.30052 \dots + 2 πn

Degrees

a = 131.81031 \dots^{\circ} + 36 0^{\circ} n, a = - 131.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- cos (a) - 11 = 2 cos (a) - 9

Solve by substitution

- cos (a) - 11 = 2 cos (a) - 9

Let:

cos (a) = u

- u - 11 = 2 u - 9

- u - 11 = 2 u - 9 : u = - \frac{2}{3}

- u - 11 = 2 u - 9

Move

11

to the right side

- u - 11 = 2 u - 9

Add

11

to both sides

- u - 11 + 11 = 2 u - 9 + 11

Simplify

- u = 2 u + 2

- u = 2 u + 2

Move

2 u

to the left side

- u = 2 u + 2

Subtract

2 u

from both sides

- u - 2 u = 2 u + 2 - 2 u

Simplify

- 3 u = 2

- 3 u = 2

Divide both sides by

- 3

- 3 u = 2

Divide both sides by

- 3

\frac{- 3 u}{- 3} = \frac{2}{- 3}

Simplify

u = - \frac{2}{3}

u = - \frac{2}{3}

Substitute back

u = cos (a)

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

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

cos (a) = - \frac{2}{3} : a = arccos (- \frac{2}{3}) + 2 πn, a = - arccos (- \frac{2}{3}) + 2 πn

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

Apply trig inverse properties

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

General solutions for

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

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

a = arccos (- \frac{2}{3}) + 2 πn, a = - arccos (- \frac{2}{3}) + 2 πn

a = arccos (- \frac{2}{3}) + 2 πn, a = - arccos (- \frac{2}{3}) + 2 πn

Combine all the solutions

a = arccos (- \frac{2}{3}) + 2 πn, a = - arccos (- \frac{2}{3}) + 2 πn

Show solutions in decimal form

a = 2.30052 \dots + 2 πn, a = - 2.30052 \dots + 2 πn

4 - 2 sin (x) = 0

sin^{2} (θ) - 2 sin (θ) + 3 = 0

3 tan^{2} (θ) + 3 tan (θ) = 0, 0^{\circ} \leq θ \leq 36 0^{\circ}

cos (a) = \frac{24}{25}

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

What is the general solution for -cos(a)-11=2cos(a)-9 ?
The general solution for -cos(a)-11=2cos(a)-9 is a=2.30052…+2pin,a=-2.30052…+2pin