What is the value of 4+3cos(-pi/6) ?

The value of 4+3cos(-pi/6) is 4+(3sqrt(3))/2

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4+3cos(-pi/6)

4 + 3 cos (- \frac{π}{6})

4 + \frac{3 3}{2}

Decimal Notation

6.59807 \dots

Solution steps

4 + 3 cos (- \frac{π}{6})

Rewrite using trig identities:

cos (- \frac{π}{6}) = \frac{3}{2}

cos (- \frac{π}{6})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{6}) = cos (\frac{π}{6})

= 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}

= \frac{3}{2}

= 4 + 3 \cdot \frac{3}{2}

Simplify

4 + 3 \cdot \frac{3}{2} : 4 + \frac{3 3}{2}

4 + 3 \cdot \frac{3}{2}

Multiply

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

3 \cdot \frac{3}{2}

Multiply fractions:

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

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

= 4 + \frac{3 3}{2}

= 4 + \frac{3 3}{2}

cos (2 π^{50}) \cdot \frac{100}{π}

- cos (\frac{3 π}{4}) + cos (\frac{π}{2})

cos^{6} (0)

\frac{5}{π} - arccos (\frac{50}{110})

4 cos^{2} (6 0^{\circ}) + 3 tan (3 0^{\circ})

What is the value of 4+3cos(-pi/6) ?
The value of 4+3cos(-pi/6) is 4+(3sqrt(3))/2