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

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

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

sin (x) = 3 cos (x)

x = \frac{π}{3} + πn

Degrees

x = 6 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{π}{3} + πn

x = \frac{π}{3} + πn

cos (2 t) = cos (t)

cos (x) + cos (2 x) + cos (3 x) = 0

2 cot (θ) - 7 = 0

sec (x) = - \frac{2 3}{3}

2 cos (3 θ) = - 2

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