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

The general solution for -2+3csc(x)=5 is x=0.44291…+2pin,x=pi-0.44291…+2pin

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-2+3csc(x)=5

- 2 + 3 csc (x) = 5

x = 0.44291 \dots + 2 πn, x = π - 0.44291 \dots + 2 πn

Degrees

x = 25.37693 \dots^{\circ} + 36 0^{\circ} n, x = 154.62306 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- 2 + 3 csc (x) = 5

Move

2

to the right side

- 2 + 3 csc (x) = 5

Add

2

to both sides

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

Simplify

3 csc (x) = 7

3 csc (x) = 7

Divide both sides by

3

3 csc (x) = 7

Divide both sides by

3

\frac{3 csc ( x )}{3} = \frac{7}{3}

Simplify

csc (x) = \frac{7}{3}

csc (x) = \frac{7}{3}

Apply trig inverse properties

csc (x) = \frac{7}{3}

General solutions for

csc (x) = \frac{7}{3}

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

x = arccsc (\frac{7}{3}) + 2 πn, x = π - arccsc (\frac{7}{3}) + 2 πn

x = arccsc (\frac{7}{3}) + 2 πn, x = π - arccsc (\frac{7}{3}) + 2 πn

Show solutions in decimal form

x = 0.44291 \dots + 2 πn, x = π - 0.44291 \dots + 2 πn

2 sin (2 x) = sin (4 x), 0 \leq x \leq π

9 sin (x) - 2 = 4 sin^{2} (x)

- a c_{1} sin (a x) + a c_{2} cos (a x) = 0

3 - 3 cos (x) = 0

- 2 cot (x) = csc^{2} (x)

What is the general solution for -2+3csc(x)=5 ?
The general solution for -2+3csc(x)=5 is x=0.44291…+2pin,x=pi-0.44291…+2pin