What is the value of tan(arccos((-12)/(13))) ?

The value of tan(arccos((-12)/(13))) is -5/12

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tan(arccos((-12)/(13)))

tan (arccos (\frac{- 12}{13}))

- \frac{5}{12}

Decimal Notation

- 0.41666 \dots

Solution steps

tan (arccos (\frac{- 12}{13}))

Rewrite using trig identities:

tan (arccos (\frac{- 12}{13})) = \frac{1 - ( \frac{- 12}{13} ) ^{2}}{( \frac{- 12}{13} )}

Use the following identity:

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

= \frac{1 - ( \frac{- 12}{13} ) ^{2}}{( \frac{- 12}{13} )}

= \frac{1 - ( \frac{- 12}{13} ) ^{2}}{\frac{- 12}{13}}

Simplify

= - \frac{5}{12}

- π sin (2 π)

\frac{sin ( 4 0 ^{\circ} )}{sin ( 2 5 ^{\circ} )}

cos (\frac{π}{2} 2)

50 sin (1 0^{\circ})

arcsin (\frac{25}{45})

What is the value of tan(arccos((-12)/(13))) ?
The value of tan(arccos((-12)/(13))) is -5/12