What is the value of cos(465) ?

The value of cos(465) is (sqrt(2)(1-sqrt(3)))/4

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cos(465)

cos (46 5^{\circ})

\frac{2 ( 1 - 3 )}{4}

Solution steps

cos (46 5^{\circ})

cos (46 5^{\circ}) = cos (10 5^{\circ})

= cos (10 5^{\circ})

Rewrite using trig identities:

cos (6 0^{\circ}) cos (4 5^{\circ}) - sin (6 0^{\circ}) sin (4 5^{\circ})

= cos (6 0^{\circ}) cos (4 5^{\circ}) - sin (6 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

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

Simplify

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

= \frac{2 ( 1 - 3 )}{4}

arccos (sin (\frac{5 π}{2}))

4 sin (18 0^{\circ})

sin (\frac{7 π}{8}) - sin (\frac{7 π}{6}) - cot (\frac{π}{3})

2 sin (6 0^{\circ}) sec (3 0^{\circ}) cos (4 5^{\circ}) tan (4 5^{\circ})

3 + 2 sin (\frac{π}{4})