What is the general solution for csc(x)=-3/(sqrt(5)) ?

The general solution for csc(x)=-3/(sqrt(5)) is x=-0.84106…+2pin,x=pi+0.84106…+2pin

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csc(x)=-3/(sqrt(5))

csc (x) = - \frac{3}{5}

x = - 0.84106 \dots + 2 πn, x = π + 0.84106 \dots + 2 πn

Radians

x = - 0.84106 \dots + 6.28318 \dots n, x = π + 0.84106 \dots + 6.28318 \dots n

Solution steps

csc (x) = - \frac{3}{5}

Simplify

- \frac{3}{5} : - \frac{3 5}{5}

- \frac{3}{5}

Multiply by the conjugate

\frac{5}{5}

= - \frac{3 5}{5 5}

55 = 5

55

Apply radical rule:

a a = a

55 = 5

= 5

= - \frac{3 5}{5}

csc (x) = - \frac{3 5}{5}

Apply trig inverse properties

csc (x) = - \frac{3 5}{5}

General solutions for

csc (x) = - \frac{3 5}{5}

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

x = arccsc (- \frac{3 5}{5}) + 2 πn, x = π + arccsc (\frac{3 5}{5}) + 2 πn

x = arccsc (- \frac{3 5}{5}) + 2 πn, x = π + arccsc (\frac{3 5}{5}) + 2 πn

Show solutions in decimal form

x = - 0.84106 \dots + 2 πn, x = π + 0.84106 \dots + 2 πn

cos (x) = \frac{3}{5}, cos (2 π + x)

sin (4 5^{\circ}) = 1.57 \cdot sin (θ)

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

3 (cos (x) - 1) = - 1

9.6 8^{2} = 12. 5^{2} + 6.4 7^{2} - 2 \cdot 12.5 \cdot 6.47 \cdot cos (θ)

What is the general solution for csc(x)=-3/(sqrt(5)) ?
The general solution for csc(x)=-3/(sqrt(5)) is x=-0.84106…+2pin,x=pi+0.84106…+2pin