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

Solution steps

3 cos (θ) + 2 = 0

Move

2

to the right side

3 cos (θ) = - 2

Divide both sides by

3

cos (θ) = - \frac{2}{3}

Apply trig inverse properties

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