What is the value of tan(150) ?

The value of tan(150) is -(sqrt(3))/3

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tan(150)

tan (15 0^{\circ})

- \frac{3}{3}

Solution steps

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}

tan (\frac{4 π}{3})

cos (2 x) = \frac{2}{2}

cos (x) = \frac{1}{2}

2 cos (θ) + 1 = 0

cos^{2} (x) - sin^{2} (x) = 2 cos^{2} (x) - 1