What is the general solution for csc(x)=sqrt(2),0<= x<= 2pi ?

The general solution for csc(x)=sqrt(2),0<= x<= 2pi is x= pi/4 ,x=(3pi)/4

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csc(x)=sqrt(2),0<= x<= 2pi

csc (x) = 2, 0 \leq x \leq 2 π

x = \frac{π}{4}, x = \frac{3 π}{4}

Degrees

x = 4 5^{\circ}, x = 13 5^{\circ}

Solution steps

csc (x) = 2, 0 \leq x \leq 2 π

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

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{4}, x = \frac{3 π}{4}

tan (x) = \frac{2}{3}

3 sec (x) - 2 = 0

(tan (x) + 1) (2 cos (x) - 3) = 0

sin (2 x) = 2 cos (x)

\frac{2}{2} csc (x) - 1 = 0

What is the general solution for csc(x)=sqrt(2),0<= x<= 2pi ?
The general solution for csc(x)=sqrt(2),0<= x<= 2pi is x= pi/4 ,x=(3pi)/4