What is the value of tan(1380) ?

The value of tan(1380) is -sqrt(3)

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tan(1380)

tan (138 0^{\circ})

- 3

Solution steps

tan (138 0^{\circ})

tan (138 0^{\circ}) = tan (12 0^{\circ})

= tan (12 0^{\circ})

Rewrite using trig identities:

\frac{sin ( 12 0 ^{\circ} )}{cos ( 12 0 ^{\circ} )}

= \frac{sin ( 12 0 ^{\circ} )}{cos ( 12 0 ^{\circ} )}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

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

Simplify

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

= - 3

(cot (\frac{π}{4}))^{\frac{7}{4}}

sec (5 2^{\circ})

- 4 sin (2 (\frac{π}{4}))

2 sec (\frac{π}{6})

8 sin (2 0^{\circ})