What is the general solution for 3cos(θ)+sqrt(2)=0 ?

The general solution for 3cos(θ)+sqrt(2)=0 is θ=2.06167…+2pin,θ=-2.06167…+2pin

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3cos(θ)+sqrt(2)=0

3 cos (θ) + 2 = 0

θ = 2.06167 \dots + 2 πn, θ = - 2.06167 \dots + 2 πn

Degrees

θ = 118.12550 \dots^{\circ} + 36 0^{\circ} n, θ = - 118.12550 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (θ) + 2 = 0

Move

2

to the right side

3 cos (θ) + 2 = 0

Subtract

2

from both sides

3 cos (θ) + 2 - 2 = 0 - 2

Simplify

3 cos (θ) = - 2

3 cos (θ) = - 2

Divide both sides by

3

3 cos (θ) = - 2

Divide both sides by

3

\frac{3 cos ( θ )}{3} = \frac{- 2}{3}

Simplify

cos (θ) = - \frac{2}{3}

cos (θ) = - \frac{2}{3}

Apply trig inverse properties

cos (θ) = - \frac{2}{3}

General solutions for

cos (θ) = - \frac{2}{3}

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

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

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

Show solutions in decimal form

θ = 2.06167 \dots + 2 πn, θ = - 2.06167 \dots + 2 πn

- cot (x) - 3 cos (x) = - cot (x) cos (x) - 3 cos (x)

6 cos^{2} (x) + 3 cos (x) = 0

6 sin (A) + 4 = 2 sin (A) + 8

(cot (x) - 3) (2 sin (x) + 1) = 0

x, tan (x) = 3

What is the general solution for 3cos(θ)+sqrt(2)=0 ?
The general solution for 3cos(θ)+sqrt(2)=0 is θ=2.06167…+2pin,θ=-2.06167…+2pin