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

The value of tan(arccos((-2)/3)) is -(sqrt(5))/2

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

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

- \frac{5}{2}

Decimal Notation

- 1.11803 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{5}{2}

tan^{2} (3 5^{\circ})

cot (- 7 π)

arcsin (\frac{7}{3})

\frac{0.035 \cdot 9.8}{cos ( 6 5 ^{\circ} )}

1 - 2 cos (2 π)

What is the value of tan(arccos((-2)/3)) ?
The value of tan(arccos((-2)/3)) is -(sqrt(5))/2