What is the general solution for csc(x)=sqrt(2) ?

The general solution for csc(x)=sqrt(2) is x= pi/4+2pin,x=(3pi)/4+2pin

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csc(x)=sqrt(2)

csc (x) = 2

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Degrees

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

Solution steps

csc (x) = 2

General solutions for

csc (x) = 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

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

4 cos^{2} (θ) = 1

sin (x) = \frac{1}{2}

2 sin (x) = 2

cot (θ) = 1

sec^{2} (x) - 1 = 0

What is the general solution for csc(x)=sqrt(2) ?
The general solution for csc(x)=sqrt(2) is x= pi/4+2pin,x=(3pi)/4+2pin