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

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

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sqrt(3)cos(x)+sin(x)=0

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

x = \frac{2 π}{3} + πn

Degrees

x = 12 0^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{3 cos ( x ) + sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

3 + \frac{sin ( x )}{cos ( x )} = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

3 + tan (x) = 0

3 + tan (x) = 0

Move

3

to the right side

3 + tan (x) = 0

Subtract

3

from both sides

3 + tan (x) - 3 = 0 - 3

Simplify

tan (x) = - 3

tan (x) = - 3

General solutions for

tan (x) = - 3

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

3 sec (2 x) = 2

cos^{2} (x) = - \frac{1}{2}

sin (6 x) = - \frac{1}{2}

2 sin^{2} (θ) + 1 = 3 sin (θ)

sin^{2} (x) = \frac{1}{2}, 0 \leq x \leq 2 π

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