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

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

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

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

x = \frac{π}{3} + πn

Degrees

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

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

- tan (x) + 3 = 0

- tan (x) + 3 = 0

Move

3

to the right side

- tan (x) + 3 = 0

Subtract

3

from both sides

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

Simplify

- tan (x) = - 3

- tan (x) = - 3

Divide both sides by

- 1

- tan (x) = - 3

Divide both sides by

- 1

\frac{- tan ( x )}{- 1} = \frac{- 3}{- 1}

Simplify

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

tan (b) = \frac{5}{12}

sin (θ) = \frac{35}{37}

sin^{2} (θ) = \frac{2 + 3}{4}

8 sin (c) + 3 = 3 sin (c) + 3

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

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