What is the general solution for 3csc(x)-4=0 ?

The general solution for 3csc(x)-4=0 is x=0.84806…+2pin,x=pi-0.84806…+2pin

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3csc(x)-4=0

3 csc (x) - 4 = 0

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

Solution steps

3 csc (x) - 4 = 0

Move

4

to the right side

3 csc (x) = 4

Divide both sides by

3

csc (x) = \frac{4}{3}

Apply trig inverse properties

x = arccsc (\frac{4}{3}) + 2 πn, x = π - arccsc (\frac{4}{3}) + 2 πn

Show solutions in decimal form

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

sin (x) = \frac{7}{8}

3 cos (2 x) - 2 cos^{2} (x) - 5 = 2 cos^{2} (x) - 7

sin (3 x + 48) = cos (1 0^{\circ} - x)

0 = sin (5 x)

2 sin (\frac{θ}{3}) + 3 = 0, 0 \leq θ \leq 2 π

What is the general solution for 3csc(x)-4=0 ?
The general solution for 3csc(x)-4=0 is x=0.84806…+2pin,x=pi-0.84806…+2pin