What is the value of tan(-750) ?

The value of tan(-750) is -(sqrt(3))/3

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tan(-750)

tan (- 75 0^{\circ})

- \frac{3}{3}

Decimal Notation

- 0.57735 \dots

Solution steps

tan (- 75 0^{\circ})

Use the following property:

tan (- x) = - tan (x)

tan (- 75 0^{\circ}) = - tan (75 0^{\circ})

= - tan (75 0^{\circ})

tan (75 0^{\circ}) = tan (3 0^{\circ})

tan (75 0^{\circ})

Rewrite

75 0^{\circ}

18 0^{\circ} \cdot 4 + 3 0^{\circ}

= tan (18 0^{\circ} 4 + 3 0^{\circ})

Apply the periodicity of

tan

tan (x + 18 0^{\circ} \cdot k) = tan (x)

tan (18 0^{\circ} \cdot 4 + 3 0^{\circ}) = tan (3 0^{\circ})

= tan (3 0^{\circ})

= - tan (3 0^{\circ})

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= - \frac{3}{3}

cos^{2} (\frac{π}{13}) - sin^{2} (\frac{π}{13})

\frac{sin ( 3 )}{1 - sin ( 3 )}

cos (3 \frac{π}{3})

\frac{sin ( 2 ) ( - 1.5 )}{- 1.5}

- cot (\frac{π}{6}) csc (\frac{π}{6})