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

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

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-sin(pi/6)-cos(pi/6+pi/6)

- sin (\frac{π}{6}) - cos (\frac{π}{6} + \frac{π}{6})

- 1

Solution steps

- sin (\frac{π}{6}) - 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}

= - sin (\frac{π}{6}) - cos (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

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{1}{2}

Simplify

- \frac{1}{2} - \frac{1}{2} : - 1

- \frac{1}{2} - \frac{1}{2}

Apply rule

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

= \frac{- 1 - 1}{2}

Subtract the numbers:

- 1 - 1 = - 2

= \frac{- 2}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= - 1

= - 1

\frac{( 7.51 ) ^{2} \cdot sin ( 3 0 ^{\circ} )}{9.4}

- 2 cos (- 1)

1 \cdot sin (\frac{π}{2})

arcsin (- 0.81)

3 cos (2 5^{\circ})

What is the value of -sin(pi/6)-cos(pi/6+pi/6) ?
The value of -sin(pi/6)-cos(pi/6+pi/6) is -1