What is the value of cos(-495) ?

The value of cos(-495) is -(sqrt(2))/2

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cos(-495)

cos (- 49 5^{\circ})

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

Solution steps

cos (- 49 5^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 49 5^{\circ}) = cos (49 5^{\circ})

= cos (49 5^{\circ})

cos (49 5^{\circ}) = cos (13 5^{\circ})

cos (49 5^{\circ})

Rewrite

49 5^{\circ}

36 0^{\circ} + 13 5^{\circ}

= cos (36 0^{\circ} + 13 5^{\circ})

Apply the periodicity of

cos

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

cos (36 0^{\circ} + 13 5^{\circ}) = cos (13 5^{\circ})

= cos (13 5^{\circ})

= cos (13 5^{\circ})

Use the following trivial identity:

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

cos (13 5^{\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{2}{2}

= - \frac{2}{2}

arctan (26)

csc (11 0^{\circ})

\frac{67}{tan ( 56. 3 ^{\circ} ) cos ( 12. 7 ^{\circ} ) + sin ( 12. 7 ^{\circ} )}

2 - sin (\frac{3 π}{2})

cos (11 7^{\circ})