What is the value of cos((7pi)/6) ?

The value of cos((7pi)/6) is -(sqrt(3))/2

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cos((7pi)/6)

cos (\frac{7 π}{6})

- \frac{3}{2}

Solution steps

cos (\frac{7 π}{6})

Rewrite using trig identities:

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

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

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

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

Simplify

= - \frac{3}{2}

2 cos^{2} (x) + sin (x) - 2 = 0

cos (3 π)

8 sin^{2} (x) + 2 cos (x) = 7

tan (\frac{19 π}{12})

\frac{1}{sec ( x ) - tan ( x )} = sec (x) + tan (x)