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Popular >

tan(5/4 pi)

Solution

tan (\frac{5}{4} π)

Solution

1

Solution steps

tan (\frac{5}{4} π)

Simplify:

\frac{5}{4} π = \frac{5 π}{4}

\frac{5}{4} π

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 π}{4}

= tan (\frac{5 π}{4})

tan (\frac{5 π}{4}) = tan (\frac{π}{4})

tan (\frac{5 π}{4})

Rewrite

\frac{5 π}{4}

as

π + \frac{π}{4}

= tan (π + \frac{π}{4})

Apply the periodicity of

tan

:

tan (x + π) = tan (x)

tan (π + \frac{π}{4}) = tan (\frac{π}{4})

= tan (\frac{π}{4})

= tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

Popular Examples

arctan (0.92)

50 sin (7 0^{\circ})

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\frac{12.1}{sin ( 2 4 ^{\circ} )}

arctan (0.43)

sin(pi/(12))-sin((5pi)/(12))

sin (\frac{π}{12}) - sin (\frac{5 π}{12})

Frequently Asked Questions (FAQ)

What is the value of tan(5/4 pi) ?
The value of tan(5/4 pi) is 1