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

The general solution for 3sin(x)=sqrt(3)cos(x) is x= pi/6+pin

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

3 sin (x) = 3 cos (x)

x = \frac{π}{6} + πn

Degrees

x = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

3 sin (x) = 3 cos (x)

Rewrite using trig identities

3 sin (x) = 3 cos (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

3 tan (x) = 3

3 tan (x) = 3

Divide both sides by

3

3 tan (x) = 3

Divide both sides by

3

\frac{3 tan ( x )}{3} = \frac{3}{3}

Simplify

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3}

General solutions for

tan (x) = \frac{3}{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}{6} + πn

x = \frac{π}{6} + πn

- 4 sin^{2} (θ) - 7 sin (θ) + 4 = 0

cos (8 x) - cos (4 x) = 0

cos (x) = \frac{4}{3}

cos^{2} (θ) - sin (θ) cos (θ) = 0

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

What is the general solution for 3sin(x)=sqrt(3)cos(x) ?
The general solution for 3sin(x)=sqrt(3)cos(x) is x= pi/6+pin