What is the value of 1+2cos(30) ?

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

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1+2cos(30)

1 + 2 cos (3 0^{\circ})

1 + 3

Decimal Notation

2.73205 \dots

Solution steps

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

Simplify

1 + 2 \cdot \frac{3}{2} : 1 + 3

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

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

2 \cdot \frac{3}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

2

= 3

= 1 + 3

= 1 + 3

arccos (\frac{33}{65})

25.1 sin (0.8)

1 + cos^{2} (0)

3 (cos (\frac{π}{6}) + i, \frac{π}{6})

arcsin (\frac{309.4 \cdot sin ( 42.3 1 ^{\circ} )}{238.99})