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

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

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

3 \cdot sin (x) = 3 \cdot cos (x)

x = \frac{π}{3} + πn

Degrees

x = 6 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

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

Simplify

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

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

Cancel the common factor:

3

= tan (x)

Simplify

\frac{3}{3} : 3

\frac{3}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{3}{3 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= 3^{1 - \frac{1}{2}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 3^{\frac{1}{2}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= 3

tan (x) = 3

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

12 sin (3 x) = 0

sin (θ) cos (θ) = cos (θ)

tan^{2} (2 θ) = 3

tan^{2} (2 θ) = 1

(50.691) cos (50.69 1^{\circ} - c) + sin (50.69 1^{\circ} - c) = 0

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