What is the general solution for 2csc(A)-4=0 ?

The general solution for 2csc(A)-4=0 is A= pi/6+2pin,A=(5pi)/6+2pin

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2csc(A)-4=0

2 csc (A) - 4 = 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

2 csc (A) - 4 = 0

Move

4

to the right side

2 csc (A) - 4 = 0

Add

4

to both sides

2 csc (A) - 4 + 4 = 0 + 4

Simplify

2 csc (A) = 4

2 csc (A) = 4

Divide both sides by

2

2 csc (A) = 4

Divide both sides by

2

\frac{2 csc ( A )}{2} = \frac{4}{2}

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

7 tan^{2} (x) - 21 = 0

- 4 cos (x) = - sin^{2} (x) + 4

sin (x) cos (x) + sin (x) = 0

sin (θ) = 0.56

cos (x) - 5 sin (2 x) = 0

What is the general solution for 2csc(A)-4=0 ?
The general solution for 2csc(A)-4=0 is A= pi/6+2pin,A=(5pi)/6+2pin