What is the value of csc(540) ?

The value of csc(540) is Undefined

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csc(540)

csc (54 0^{\circ})

Undefined

Solution steps

csc (54 0^{\circ})

csc (54 0^{\circ}) = csc (18 0^{\circ})

csc (54 0^{\circ})

Rewrite

54 0^{\circ}

36 0^{\circ} + 18 0^{\circ}

= csc (36 0^{\circ} + 18 0^{\circ})

Apply the periodicity of

csc

csc (x + 36 0^{\circ}) = csc (x)

csc (36 0^{\circ} + 18 0^{\circ}) = csc (18 0^{\circ})

= csc (18 0^{\circ})

= csc (18 0^{\circ})

Rewrite using trig identities:

Undefined

csc (18 0^{\circ})

Use the basic trigonometric identity:

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

= \frac{1}{sin ( 18 0 ^{\circ} )}

Simplify

\frac{1}{sin ( 18 0 ^{\circ} )} :

Undefined

\frac{1}{sin ( 18 0 ^{\circ} )}

sin (18 0^{\circ}) = 0

= \frac{1}{0}

\frac{x}{0}

is undefined

= Undefined

= Undefined

= Undefined

tan (60 0^{\circ})

cos (25 5^{\circ}) - cos (19 5^{\circ})

1 - 2 sin^{2} (1 5^{\circ})

cos (\frac{5}{4} π)

cot (4)