What is the value of (5pi)/6+2cos((5pi)/6) ?

The value of (5pi)/6+2cos((5pi)/6) is (5pi)/6-sqrt(3)

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(5pi)/6+2cos((5pi)/6)

\frac{5 π}{6} + 2 cos (\frac{5 π}{6})

\frac{5 π}{6} - 3

Decimal Notation

0.88594 \dots

Solution steps

\frac{5 π}{6} + 2 cos (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

cos (\frac{5 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{5 π}{6} + 2 (- \frac{3}{2})

Simplify

\frac{5 π}{6} + 2 (- \frac{3}{2}) : \frac{5 π}{6} - 3

\frac{5 π}{6} + 2 (- \frac{3}{2})

Remove parentheses:

(- a) = - a

= \frac{5 π}{6} - 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

= \frac{5 π}{6} - 3

= \frac{5 π}{6} - 3

arctan (\frac{0.1}{cos ( 3 )})

\frac{tan ( 5 0 ^{\circ} )}{cot ( 4 0 ^{\circ} )} + \frac{5 csc ( 2 0 ^{\circ} )}{sec ( 7 0 ^{\circ} )}

sec^{2} (arctan (2)) + csc^{2} (arccot (3))

arccos (0.375)

arccos (1.6)

What is the value of (5pi)/6+2cos((5pi)/6) ?
The value of (5pi)/6+2cos((5pi)/6) is (5pi)/6-sqrt(3)