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

The general solution for sin(θ)+sqrt(3)cos(θ)=0 is θ=(2pi)/3+pin

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sin(θ)+sqrt(3)cos(θ)=0

sin (θ) + 3 cos (θ) = 0

θ = \frac{2 π}{3} + πn

Solution steps

sin (θ) + 3 cos (θ) = 0

Rewrite using trig identities

tan (θ) + 3 = 0

Move

3

to the right side

tan (θ) = - 3

General solutions for

tan (θ) = - 3

θ = \frac{2 π}{3} + πn

cos (x) + 2 sin (x) cos (x) = 0

3 tan (x) + 3 = 0

(2 sin^{2} (x) - 1) (3 tan^{2} (x) - 1) = 0

sec (x) - 1 = 0

cos (x) + 2 sin (x) = 2

What is the general solution for sin(θ)+sqrt(3)cos(θ)=0 ?
The general solution for sin(θ)+sqrt(3)cos(θ)=0 is θ=(2pi)/3+pin