What is the value of cos(-390) ?

The value of cos(-390) is (sqrt(3))/2

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cos(-390)

cos (- 39 0^{\circ})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

cos (- 39 0^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 39 0^{\circ}) = cos (39 0^{\circ})

= cos (39 0^{\circ})

cos (39 0^{\circ}) = cos (3 0^{\circ})

cos (39 0^{\circ})

Rewrite

39 0^{\circ}

36 0^{\circ} + 3 0^{\circ}

= cos (36 0^{\circ} + 3 0^{\circ})

Apply the periodicity of

cos

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 3 0^{\circ}) = cos (3 0^{\circ})

= cos (3 0^{\circ})

= cos (3 0^{\circ})

Use the following trivial identity:

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

cos (3 0^{\circ})

cos (x)

periodicity table with

36 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= \frac{3}{2}

15 sin (6 0^{\circ})

arctan (0.04)

40 sin (3 0^{\circ})

cos (\frac{7 π}{12}) cos (\frac{5 π}{12}) + sin (\frac{7 π}{12}) sin (\frac{5 π}{12})

cot (\frac{- π}{4})