What is the value of tan(690) ?

The value of tan(690) is -(sqrt(3))/3

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tan(690)

tan (69 0^{\circ})

- \frac{3}{3}

Solution steps

tan (69 0^{\circ})

tan (69 0^{\circ}) = tan (15 0^{\circ})

= tan (15 0^{\circ})

Rewrite using trig identities:

\frac{sin ( 15 0 ^{\circ} )}{cos ( 15 0 ^{\circ} )}

= \frac{sin ( 15 0 ^{\circ} )}{cos ( 15 0 ^{\circ} )}

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

= \frac{\frac{1}{2}}{- \frac{3}{2}}

Simplify

\frac{\frac{1}{2}}{- \frac{3}{2}} : - \frac{3}{3}

= - \frac{3}{3}

\frac{4}{cos ( 2 5 ^{\circ} )}

sec (\frac{1}{2})

1000 cos (4 5^{\circ})

arctan (\frac{14}{15})

cos (4 5^{\circ}) - sin (3 0^{\circ})