What is the general solution for 3-2csc(x)=17 ?

The general solution for 3-2csc(x)=17 is x=-0.14334…+2pin,x=pi+0.14334…+2pin

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3-2csc(x)=17

3 - 2 csc (x) = 17

x = - 0.14334 \dots + 2 πn, x = π + 0.14334 \dots + 2 πn

Degrees

x = - 8.21321 \dots^{\circ} + 36 0^{\circ} n, x = 188.21321 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 - 2 csc (x) = 17

Move

3

to the right side

3 - 2 csc (x) = 17

Subtract

3

from both sides

3 - 2 csc (x) - 3 = 17 - 3

Simplify

- 2 csc (x) = 14

- 2 csc (x) = 14

Divide both sides by

- 2

- 2 csc (x) = 14

Divide both sides by

- 2

\frac{- 2 csc ( x )}{- 2} = \frac{14}{- 2}

Simplify

\frac{- 2 csc ( x )}{- 2} = \frac{14}{- 2}

Simplify

\frac{- 2 csc ( x )}{- 2} : csc (x)

\frac{- 2 csc ( x )}{- 2}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{2 csc ( x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= csc (x)

Simplify

\frac{14}{- 2} : - 7

\frac{14}{- 2}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{14}{2}

Divide the numbers:

\frac{14}{2} = 7

= - 7

csc (x) = - 7

csc (x) = - 7

csc (x) = - 7

Apply trig inverse properties

csc (x) = - 7

General solutions for

csc (x) = - 7

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

x = arccsc (- 7) + 2 πn, x = π + arccsc (7) + 2 πn

x = arccsc (- 7) + 2 πn, x = π + arccsc (7) + 2 πn

Show solutions in decimal form

x = - 0.14334 \dots + 2 πn, x = π + 0.14334 \dots + 2 πn

2 sin (x) - 1 = 0.5

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

sin (θ) = \frac{1}{2}, θ

tan (x) = \frac{40}{34}

cot (b) = - 5

What is the general solution for 3-2csc(x)=17 ?
The general solution for 3-2csc(x)=17 is x=-0.14334…+2pin,x=pi+0.14334…+2pin