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

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

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

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

\frac{- 1 + 3}{2}

Decimal Notation

0.36602 \dots

Solution steps

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

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}{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{1}{2} + \frac{3}{2}

Simplify

- \frac{1}{2} + \frac{3}{2} : \frac{- 1 + 3}{2}

- \frac{1}{2} + \frac{3}{2}

Apply rule

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

= \frac{- 1 + 3}{2}

= \frac{- 1 + 3}{2}

arccos (0.01)

4 arccos (\frac{0}{2})

250 sin (8 5^{\circ})

- \frac{1}{4} csc^{3} (\frac{π}{4})

- sin (\frac{π ^{0}}{2}) \frac{π}{2}

What is the value of -sin(pi/6)+cos(pi/6) ?
The value of -sin(pi/6)+cos(pi/6) is (-1+sqrt(3))/2