What is the general solution for (csc(x))/5 =2 ?

The general solution for (csc(x))/5 =2 is x=0.10016…+2pin,x=pi-0.10016…+2pin

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(csc(x))/5 =2

\frac{csc ( x )}{5} = 2

x = 0.10016 \dots + 2 πn, x = π - 0.10016 \dots + 2 πn

Degrees

x = 5.73917 \dots^{\circ} + 36 0^{\circ} n, x = 174.26082 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{csc ( x )}{5} = 2

Multiply both sides by

5

\frac{csc ( x )}{5} = 2

Multiply both sides by

5

\frac{5 csc ( x )}{5} = 2 \cdot 5

Simplify

csc (x) = 10

csc (x) = 10

Apply trig inverse properties

csc (x) = 10

General solutions for

csc (x) = 10

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

x = arccsc (10) + 2 πn, x = π - arccsc (10) + 2 πn

x = arccsc (10) + 2 πn, x = π - arccsc (10) + 2 πn

Show solutions in decimal form

x = 0.10016 \dots + 2 πn, x = π - 0.10016 \dots + 2 πn

cos (2 x) = \frac{( 7 k - 7 )}{3}

1 - sin (θ) = cos (θ)

32 = 37.3 sin (\frac{2 π}{365} (x - 114)) + 26

2 sin (2 x) - 1 = 0

x, 2 sin (x) - 1 = 0

What is the general solution for (csc(x))/5 =2 ?
The general solution for (csc(x))/5 =2 is x=0.10016…+2pin,x=pi-0.10016…+2pin