What is the general solution for 11csc(x)+15=9csc(x)+19 ?

The general solution for 11csc(x)+15=9csc(x)+19 is x= pi/6+2pin,x=(5pi)/6+2pin

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11csc(x)+15=9csc(x)+19

11 csc (x) + 15 = 9 csc (x) + 19

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

11 csc (x) + 15 = 9 csc (x) + 19

Solve by substitution

11 csc (x) + 15 = 9 csc (x) + 19

Let:

csc (x) = u

11 u + 15 = 9 u + 19

11 u + 15 = 9 u + 19 : u = 2

11 u + 15 = 9 u + 19

Move

15

to the right side

11 u + 15 = 9 u + 19

Subtract

15

from both sides

11 u + 15 - 15 = 9 u + 19 - 15

Simplify

11 u = 9 u + 4

11 u = 9 u + 4

Move

9 u

to the left side

11 u = 9 u + 4

Subtract

9 u

from both sides

11 u - 9 u = 9 u + 4 - 9 u

Simplify

2 u = 4

2 u = 4

Divide both sides by

2

2 u = 4

Divide both sides by

2

\frac{2 u}{2} = \frac{4}{2}

Simplify

u = 2

u = 2

Substitute back

u = csc (x)

csc (x) = 2

csc (x) = 2

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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

Combine all the solutions

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

sin^{2} (x) = \frac{tan ( x )}{2}

98 \cdot sin (θ) - 19.6 \cdot cos (θ) = 75.1

\frac{( sin ( x ) + tan ( x ) )}{1 + cos ( x )} = m \cdot sec (x)

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

\frac{sin ( 2 5 ^{\circ} )}{5} = \frac{sin ( b )}{8}

What is the general solution for 11csc(x)+15=9csc(x)+19 ?
The general solution for 11csc(x)+15=9csc(x)+19 is x= pi/6+2pin,x=(5pi)/6+2pin