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})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{7 π}{6}) = cos (\frac{7 π}{6})

= 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}

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