What is the value of cos(-165) ?

The value of cos(-165) is (-sqrt(6)-sqrt(2))/4

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cos(-165)

cos (- 16 5^{\circ})

\frac{- 6 - 2}{4}

Solution steps

cos (- 16 5^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 16 5^{\circ}) = cos (16 5^{\circ})

= cos (16 5^{\circ})

Rewrite using trig identities:

cos (13 5^{\circ}) cos (3 0^{\circ}) - sin (13 5^{\circ}) sin (3 0^{\circ})

= cos (13 5^{\circ}) cos (3 0^{\circ}) - sin (13 5^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

= (- \frac{2}{2}) \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

Simplify

(- \frac{2}{2}) \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2} : \frac{- 6 - 2}{4}

= \frac{- 6 - 2}{4}

sin^{2} (- 1)

arccos (\frac{1}{2})

tan (\frac{π}{9})

arctan (1.33)

cos (7 5^{\circ}) - cos (1 5^{\circ})