What is the general solution for 3csc(x)-6=0,0<= x<= 360 ?

The general solution for 3csc(x)-6=0,0<= x<= 360 is x=30,x=150

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3csc(x)-6=0,0<= x<= 360

3 csc (x) - 6 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

x = 3 0^{\circ}, x = 15 0^{\circ}

Radians

x = \frac{π}{6}, x = \frac{5 π}{6}

Solution steps

3 csc (x) - 6 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

Move

6

to the right side

3 csc (x) - 6 = 0

Add

6

to both sides

3 csc (x) - 6 + 6 = 0 + 6

Simplify

3 csc (x) = 6

3 csc (x) = 6

Divide both sides by

3

3 csc (x) = 6

Divide both sides by

3

\frac{3 csc ( x )}{3} = \frac{6}{3}

Simplify

csc (x) = 2

csc (x) = 2

General solutions for

csc (x) = 2

csc (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

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

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

Solutions for the range

0 \leq x \leq 36 0^{\circ}

x = 3 0^{\circ}, x = 15 0^{\circ}

tan (\frac{x}{2} + \frac{π}{3}) = - 1

- sec^{2} (x) + 1 = - 5 sec (x) - 5

sec (t) = \frac{1}{- \frac{2}{2}}

sin (x) = 0.556692

tan^{2} (x) + 4 tan (x) + 3 = 0

What is the general solution for 3csc(x)-6=0,0<= x<= 360 ?
The general solution for 3csc(x)-6=0,0<= x<= 360 is x=30,x=150