What is the general solution for (2sin(x)-1)/(3*cos(x))=0 ?

The general solution for (2sin(x)-1)/(3*cos(x))=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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(2sin(x)-1)/(3*cos(x))=0

\frac{2 sin ( x ) - 1}{3 \cdot cos ( x )} = 0

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

\frac{2 sin ( x ) - 1}{3 cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 sin (x) - 1 = 0

Move

1

to the right side

2 sin (x) - 1 = 0

Add

1

to both sides

2 sin (x) - 1 + 1 = 0 + 1

Simplify

2 sin (x) = 1

2 sin (x) = 1

Divide both sides by

2

2 sin (x) = 1

Divide both sides by

2

\frac{2 sin ( x )}{2} = \frac{1}{2}

Simplify

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2}

General solutions for

sin (x) = \frac{1}{2}

sin (x)

periodicity table with

2 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

tan (θ) = \frac{34400}{254}

2 sin (x) = - 1, - π \leq x \leq π

cot (- \frac{π}{5}) - sec (x) = 1.5

\frac{1}{cos ^{2} ( x )} + (\frac{1}{2 cos ( x )}) = 0

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

What is the general solution for (2sin(x)-1)/(3*cos(x))=0 ?
The general solution for (2sin(x)-1)/(3*cos(x))=0 is x= pi/6+2pin,x=(5pi)/6+2pin