What is the general solution for -2=3csc(2x+pi)-5 ?

The general solution for -2=3csc(2x+pi)-5 is x=pin-pi/2+pi/4

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Popular >

-2=3csc(2x+pi)-5

Solution

- 2 = 3 csc (2 x + π) - 5

Solution

x = πn - \frac{π}{2} + \frac{π}{4}

Degrees

x = - 4 5^{\circ} + 18 0^{\circ} n

Solution steps

- 2 = 3 csc (2 x + π) - 5

Switch sides

3 csc (2 x + π) - 5 = - 2

Move

5

to the right side

3 csc (2 x + π) - 5 = - 2

Add

5

to both sides

3 csc (2 x + π) - 5 + 5 = - 2 + 5

Simplify

3 csc (2 x + π) = 3

3 csc (2 x + π) = 3

Divide both sides by

3

3 csc (2 x + π) = 3

Divide both sides by

3

\frac{3 csc ( 2 x + π )}{3} = \frac{3}{3}

Simplify

csc (2 x + π) = 1

csc (2 x + π) = 1

General solutions for

csc (2 x + π) = 1

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

2 x + π = \frac{π}{2} + 2 πn

2 x + π = \frac{π}{2} + 2 πn

Solve

2 x + π = \frac{π}{2} + 2 πn : x = πn - \frac{π}{2} + \frac{π}{4}

2 x + π = \frac{π}{2} + 2 πn

Move

π

to the right side

2 x + π = \frac{π}{2} + 2 πn

Subtract

π

from both sides

2 x + π - π = \frac{π}{2} + 2 πn - π

Simplify

2 x = \frac{π}{2} + 2 πn - π

2 x = \frac{π}{2} + 2 πn - π

Divide both sides by

2

2 x = \frac{π}{2} + 2 πn - π

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2} : πn - \frac{π}{2} + \frac{π}{4}

\frac{\frac{π}{2}}{2} + \frac{2 πn}{2} - \frac{π}{2}

Group like terms

= - \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

= - \frac{π}{2} + πn + \frac{π}{4}

Group like terms

= πn - \frac{π}{2} + \frac{π}{4}

x = πn - \frac{π}{2} + \frac{π}{4}

x = πn - \frac{π}{2} + \frac{π}{4}

x = πn - \frac{π}{2} + \frac{π}{4}

x = πn - \frac{π}{2} + \frac{π}{4}

Popular Examples

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cos (A) = \frac{5}{9}

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

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

solvefor x,y=sin(3x+4y)solve for

x, y = sin (3 x + 4 y)

cos(x)=0.56

cos (x) = 0.56

3-cot^2(x)=0

3 - cot^{2} (x) = 0

Frequently Asked Questions (FAQ)

What is the general solution for -2=3csc(2x+pi)-5 ?
The general solution for -2=3csc(2x+pi)-5 is x=pin-pi/2+pi/4