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

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

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-cos(pi/6+pi/6)

- cos (\frac{π}{6} + \frac{π}{6})

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

- cos (\frac{π}{6} + \frac{π}{6})

Simplify:

\frac{π}{6} + \frac{π}{6} = \frac{π}{3}

\frac{π}{6} + \frac{π}{6}

Apply rule

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

= \frac{π + π}{6}

Add similar elements:

π + π = 2 π

= \frac{2 π}{6}

Cancel the common factor:

2

= \frac{π}{3}

= - cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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{1}{2}

= - \frac{1}{2}

\frac{sin ^{3} ( π )}{3} - \frac{sin ^{3} ( 0 )}{3}

sin (4 π^{2})

10 \cdot sin (1 0^{\circ})

1 \cdot sin (0)

1 \cdot sin (1)