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

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

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

3 cos (x) = sin (x)

x = \frac{π}{3} + πn

Degrees

x = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

3 cos (x) = sin (x)

Rewrite using trig identities

3 cos (x) = sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

3 = tan (x)

Switch sides

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

- 2 sin^{2} (x) + cos (x) + 1 = 0

sin (x) tan (x) = 2 tan (x)

tan^{2} (x) - 2 tan (x) = 0

sin^{2} (θ) = 1

sin^{2} (x) - 5 cos (x) + 5 = 0

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