What is the value of cot(arccos((-3)/4)) ?

The value of cot(arccos((-3)/4)) is -(3sqrt(7))/7

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cot(arccos((-3)/4))

cot (arccos (\frac{- 3}{4}))

- \frac{3 7}{7}

Decimal Notation

- 1.13389 \dots

Solution steps

cot (arccos (\frac{- 3}{4}))

Rewrite using trig identities:

cot (arccos (\frac{- 3}{4})) = \frac{( \frac{- 3}{4} )}{1 - ( \frac{- 3}{4} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{- 3}{4} )}{1 - ( \frac{- 3}{4} ) ^{2}}

= \frac{\frac{- 3}{4}}{1 - ( \frac{- 3}{4} ) ^{2}}

Simplify

= - \frac{3 7}{7}

sin (168 0^{\circ})

arcsin (0.545)

1 - cos (\frac{2 π}{3})

- π^{2} cos (2 π)

\frac{1}{sin ( 2 0 ^{\circ} )}

What is the value of cot(arccos((-3)/4)) ?
The value of cot(arccos((-3)/4)) is -(3sqrt(7))/7