What is the value of csc(7pi) ?

The value of csc(7pi) is Undefined

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csc(7pi)

csc (7 π)

Undefined

Solution steps

csc (7 π)

csc (7 π) = csc (π)

csc (7 π)

Rewrite

7 π

2 π \cdot 3 + π

= csc (2 π 3 + π)

Apply the periodicity of

csc

csc (x + 2 π \cdot k) = csc (x)

csc (2 π \cdot 3 + π) = csc (π)

= csc (π)

= csc (π)

Rewrite using trig identities:

Undefined

csc (π)

Use the basic trigonometric identity:

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

= \frac{1}{sin ( π )}

Simplify

\frac{1}{sin ( π )} :

Undefined

\frac{1}{sin ( π )}

sin (π) = 0

= \frac{1}{0}

\frac{x}{0}

is undefined

= Undefined

= Undefined

= Undefined

cos (sin (0))

6^{2} + 8^{2} + 2 \cdot 6 \cdot 8 \cdot cos (9 0^{\circ})

tan (\frac{2 π}{3} + \frac{π}{4})

tan (0.24 π)

\frac{50}{tan ( 2 0 ^{\circ} )}