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}

cos (3 0^{\circ})

2 cos (π)

sin^{2} (\frac{π}{4})

arcsin (\frac{1}{2})

tan (3 x) = 1

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