What is the general solution for 3csc(A)-6=0 ?

The general solution for 3csc(A)-6=0 is A= pi/6+2pin,A=(5pi)/6+2pin

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3csc(A)-6=0

3 csc (A) - 6 = 0

A = \frac{π}{6} + 2 πn, A = \frac{5 π}{6} + 2 πn

Degrees

A = 3 0^{\circ} + 36 0^{\circ} n, A = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

3 csc (A) - 6 = 0

Move

6

to the right side

3 csc (A) - 6 = 0

Add

6

to both sides

3 csc (A) - 6 + 6 = 0 + 6

Simplify

3 csc (A) = 6

3 csc (A) = 6

Divide both sides by

3

3 csc (A) = 6

Divide both sides by

3

\frac{3 csc ( A )}{3} = \frac{6}{3}

Simplify

csc (A) = 2

csc (A) = 2

General solutions for

csc (A) = 2

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

A = \frac{π}{6} + 2 πn, A = \frac{5 π}{6} + 2 πn

A = \frac{π}{6} + 2 πn, A = \frac{5 π}{6} + 2 πn

15 cos^{2} (x) + sin (x) - 9 = 0

tan (x) = 2 - 3

\frac{tan ( x ) - 1}{1 + tan ( x )} = 0

arccos (x) + arccos (2 x) = \frac{π}{2}

sin^{2} (x) + sin (x) = cos^{2} (x)

What is the general solution for 3csc(A)-6=0 ?
The general solution for 3csc(A)-6=0 is A= pi/6+2pin,A=(5pi)/6+2pin