What is the general solution for 7csc(x)-3=11 ?

The general solution for 7csc(x)-3=11 is x= pi/6+2pin,x=(5pi)/6+2pin

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7csc(x)-3=11

7 csc (x) - 3 = 11

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

7 csc (x) - 3 = 11

Move

3

to the right side

7 csc (x) - 3 = 11

Add

3

to both sides

7 csc (x) - 3 + 3 = 11 + 3

Simplify

7 csc (x) = 14

7 csc (x) = 14

Divide both sides by

7

7 csc (x) = 14

Divide both sides by

7

\frac{7 csc ( x )}{7} = \frac{14}{7}

Simplify

csc (x) = 2

csc (x) = 2

General solutions for

csc (x) = 2

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 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

2 cos^{3} (x) - 1 = 0

\frac{1 - tan ^{2} ( θ )}{1 + tan ^{2} ( θ )} = 2 cos^{2} (- 1)

sin (x) = - \frac{5}{6}

5 cot (x) + 3 = 8

cos (x) = - \frac{3}{2}, 0 \leq x \leq 2 π

What is the general solution for 7csc(x)-3=11 ?
The general solution for 7csc(x)-3=11 is x= pi/6+2pin,x=(5pi)/6+2pin