What is the value of (sec(5pi))/4 ?

The value of (sec(5pi))/4 is -1/4

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(sec(5pi))/4

\frac{sec ( 5 π )}{4}

- \frac{1}{4}

Decimal Notation

- 0.25

Solution steps

\frac{sec ( 5 π )}{4}

Rewrite using trig identities:

sec (5 π) = - 1

sec (5 π)

sec (5 π) = sec (π)

sec (5 π)

Rewrite

5 π

2 π \cdot 2 + π

= sec (2 π 2 + π)

Apply the periodicity of

sec

sec (x + 2 π \cdot k) = sec (x)

sec (2 π \cdot 2 + π) = sec (π)

= sec (π)

= sec (π)

Use the following trivial identity:

sec (π) = (- 1)

sec (π)

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= (- 1)

= - 1

= \frac{- 1}{4}

Simplify

= - \frac{1}{4}

tan (- 6 π)

- \frac{π}{2} cos (\frac{π}{2}) + sin (\frac{π}{2})

\frac{2}{π \cdot 0.7} tan (\frac{π \cdot 0.7}{2})

sin (14.4 8^{\circ})

[2 (cos (\frac{π}{6}) + i sin (\frac{π}{6}))]^{3}