What is the value of tan((19pi)/4) ?

The value of tan((19pi)/4) is -1

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tan((19pi)/4)

tan (\frac{19 π}{4})

- 1

Solution steps

tan (\frac{19 π}{4})

tan (\frac{19 π}{4}) = tan (\frac{3 π}{4})

= tan (\frac{3 π}{4})

Rewrite using trig identities:

\frac{sin ( \frac{3 π}{4} )}{cos ( \frac{3 π}{4} )}

= \frac{sin ( \frac{3 π}{4} )}{cos ( \frac{3 π}{4} )}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

= \frac{\frac{2}{2}}{- \frac{2}{2}}

Simplify

\frac{\frac{2}{2}}{- \frac{2}{2}} : - 1

= - 1

cos (- 39 0^{\circ})

15 sin (6 0^{\circ})

arctan (0.04)

40 sin (3 0^{\circ})

cos (\frac{7 π}{12}) cos (\frac{5 π}{12}) + sin (\frac{7 π}{12}) sin (\frac{5 π}{12})