What is the value of cos((23pi)/6) ?

The value of cos((23pi)/6) is (sqrt(3))/2

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cos((23pi)/6)

cos (\frac{23 π}{6})

\frac{3}{2}

Solution steps

cos (\frac{23 π}{6})

cos (\frac{23 π}{6}) = cos (\frac{11 π}{6})

= cos (\frac{11 π}{6})

Rewrite using trig identities:

cos (π) cos (\frac{5 π}{6}) - sin (π) sin (\frac{5 π}{6})

= cos (π) cos (\frac{5 π}{6}) - sin (π) sin (\frac{5 π}{6})

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

= (- 1) (- \frac{3}{2}) - 0 \cdot \frac{1}{2}

Simplify

= \frac{3}{2}

cos (6 8^{\circ})

cos^{2} (4)

2 sin (4 5^{\circ})

cot (- 30 0^{\circ})

arctan (\frac{1}{8})