What is the general solution for 3csc(x)-7=0 ?

The general solution for 3csc(x)-7=0 is x=0.44291…+2pin,x=pi-0.44291…+2pin

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3csc(x)-7=0

3 csc (x) - 7 = 0

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

3 csc (x) - 7 = 0

Move

7

to the right side

3 csc (x) - 7 = 0

Add

7

to both sides

3 csc (x) - 7 + 7 = 0 + 7

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

tan (2 θ) = 0.6583

sin (x) = \frac{8}{12.8}

3 tan^{2} (x) - 2 = 5 sec^{2} (x) - 9

x, z = arcsin^{3} (3 x + 2 y)

(3 sec (θ) - 23) (2 sin (θ) - 1) = 0, 2 π

What is the general solution for 3csc(x)-7=0 ?
The general solution for 3csc(x)-7=0 is x=0.44291…+2pin,x=pi-0.44291…+2pin