What is the general solution for (sin(x)-sqrt(3)*cos(x))/2 =0 ?

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

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(sin(x)-sqrt(3)*cos(x))/2 =0

\frac{sin ( x ) - 3 \cdot cos ( x )}{2} = 0

x = \frac{π}{3} + πn

Degrees

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

Solution steps

\frac{sin ( x ) - 3 cos ( x )}{2} = 0

Rewrite using trig identities

\frac{sin ( x ) - 3 cos ( x )}{2} = 0

Divide both sides by

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

\frac{\frac{s i n ( x ) - 3 c o s ( x )}{2}}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{sin ( x )}{2 cos ( x )} - \frac{3}{2} = 0

Use the basic trigonometric identity:

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

\frac{tan ( x ) - 3}{2} = 0

\frac{tan ( x ) - 3}{2} = 0

Multiply both sides by

2

\frac{tan ( x ) - 3}{2} = 0

Multiply both sides by

2

\frac{2 ( tan ( x ) - 3 )}{2} = 0 \cdot 2

Simplify

tan (x) - 3 = 0

tan (x) - 3 = 0

Move

3

to the right side

tan (x) - 3 = 0

Add

3

to both sides

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

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

cos (\frac{1}{3 x}) = \frac{1}{3}

arctan (1 + x) + arctan (1 - x) = arctan (\frac{1}{2})

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

sin^{2} (x) - 4 sin^{2} (x) + 7 cos^{2} (x) = 0

(sin (x)) (cos (x)) = 0

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