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}

sec (3 0^{\circ}) + cot (6 0^{\circ})

csc (\frac{21 π}{10})

arctan (- \frac{23}{2})

sin (\frac{1}{\frac{2}{3 π}})

sin (1 5^{\circ}) cos (7 5^{\circ})

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