What is the value of 1+cos(30) ?

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

1+cos(30)

1 + cos (3 0^{\circ})

1 + \frac{3}{2}

Decimal

1.86602 \dots

Solution steps

1 + 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 + \frac{3}{2}

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

- arctan (\frac{1 0 ^{- 1} \cdot 10}{- 1 0 ^{- 8} \cdot 1 0 ^{2} + 1})

[arcsec (\frac{5}{3}) + arcsin (\frac{5}{13})]

\frac{3}{tan ( 1 5 ^{\circ} )}

5 sin^{2} (\frac{3 π}{2})