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

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

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sin(x)=-sqrt(3)cos(x)

sin (x) = - 3 cos (x)

x = \frac{2 π}{3} + πn

Degrees

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

Solution steps

sin (x) = - 3 cos (x)

Rewrite using trig identities

sin (x) = - 3 cos (x)

Divide both sides by

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

\frac{sin ( x )}{cos ( x )} = \frac{- 3 cos ( x )}{cos ( x )}

Simplify

\frac{sin ( x )}{cos ( x )} = - 3

Use the basic trigonometric identity:

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

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

4 sin^{2} (x) + 2 cos^{2} (x) = 3, 0 \leq x \leq 2 π

sin (x) = - 5

sin (x) = 10

tan (A) = - \frac{3}{91}

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

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