What is the value of tan(arccos(-(sqrt(3))/2)) ?

The value of tan(arccos(-(sqrt(3))/2)) is -(sqrt(3))/3

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tan(arccos(-(sqrt(3))/2))

tan (arccos (- \frac{3}{2}))

- \frac{3}{3}

Decimal Notation

- 0.57735 \dots

Solution steps

tan (arccos (- \frac{3}{2}))

Rewrite using trig identities:

tan (arccos (- \frac{3}{2})) = \frac{1 - ( - \frac{3}{2} ) ^{2}}{( - \frac{3}{2} )}

Use the following identity:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( - \frac{3}{2} ) ^{2}}{( - \frac{3}{2} )}

= \frac{1 - ( - \frac{3}{2} ) ^{2}}{- \frac{3}{2}}

Simplify

= - \frac{3}{3}

cos (\frac{5 π}{12})

sin^{2} (x) = 1

sinh (π)

cos (\frac{2 π}{2})

sin (x) = - 0.25

What is the value of tan(arccos(-(sqrt(3))/2)) ?
The value of tan(arccos(-(sqrt(3))/2)) is -(sqrt(3))/3