What is the general solution for sqrt(3)sin(x)+3cos(x)=0 ?

The general solution for sqrt(3)sin(x)+3cos(x)=0 is x=(2pi)/3+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(3)sin(x)+3cos(x)=0

Solution

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

Solution

x = \frac{2 π}{3} + πn

Degrees

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

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

\frac{3 sin ( x ) + 3 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{3 sin ( x )}{cos ( x )} + 3 = 0

Use the basic trigonometric identity:

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

3 tan (x) + 3 = 0

3 tan (x) + 3 = 0

Move

3

to the right side

3 tan (x) + 3 = 0

Subtract

3

from both sides

3 tan (x) + 3 - 3 = 0 - 3

Simplify

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 the fraction rule:

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

= - \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{2 π}{3} + πn

x = \frac{2 π}{3} + πn

Popular Examples

4sin(2x)+4cos(x)=0

4 sin (2 x) + 4 cos (x) = 0

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

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

2cos(x)=tan(x)+sec(x)

2 cos (x) = tan (x) + sec (x)

sin^2(x)cos(x)= 2/(3pi)

sin^{2} (x) cos (x) = \frac{2}{3 π}

tan(φ)=-1/(sqrt(6))

tan (φ) = - \frac{1}{6}

Frequently Asked Questions (FAQ)

What is the general solution for sqrt(3)sin(x)+3cos(x)=0 ?
The general solution for sqrt(3)sin(x)+3cos(x)=0 is x=(2pi)/3+pin