What is the value of cos(1110) ?

The value of cos(1110) is (sqrt(3))/2

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cos(1110)

cos (111 0^{\circ})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

cos (111 0^{\circ})

cos (111 0^{\circ}) = cos (3 0^{\circ})

cos (111 0^{\circ})

Rewrite

111 0^{\circ}

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

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

Apply the periodicity of

cos

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

cos (36 0^{\circ} \cdot 3 + 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}

sin (2 arctan (4))

sec (- \frac{7 π}{2})

\frac{10}{sin ( 4 5 ^{\circ} )}

9 sin (7 5^{\circ})

sin (arcsin (- 1))