What is the value of 1cos(30) ?

The value of 1cos(30) is (sqrt(3))/2

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1cos(30)

1 cos (3 0^{\circ})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

1 \cdot 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}

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

Simplify

= \frac{3}{2}

[sin^{2} (4 5^{\circ}) cos^{2} (4 5^{\circ})]^{\frac{3}{2}}

cos (11 1^{\circ}) + sin (11 1^{\circ})

\frac{cos ( 3 0 ^{\circ} )}{sin ( 6 0 ^{\circ} ) + cos ( 4 5 ^{\circ} )}

6 (cos (\frac{π}{2}) + i sin (\frac{π}{2}))

cos^{2} (0) - 3 sin (0)