What is the value of 1+2cos(pi/6) ?

The value of 1+2cos(pi/6) is 1+sqrt(3)

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1+2cos(pi/6)

1 + 2 cos (\frac{π}{6})

1 + 3

Decimal Notation

2.73205 \dots

Solution steps

1 + 2 cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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

\frac{cos ( \frac{11 π}{6} )}{sin ( \frac{11 π}{6} )}

3 + 2 sin (\frac{3 π}{2})

12.4 - 10 (0.5 π - arcsin (0.5) - 0.5 (1 - (0.5)^{2})^{\frac{1}{2}})

sin (\frac{11}{9}) π

\frac{1.24}{tan ( 3 4 ^{\circ} )}