What is the value of tan(arccos(-4/5)) ?

The value of tan(arccos(-4/5)) is -3/4

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tan(arccos(-4/5))

tan (arccos (- \frac{4}{5}))

- \frac{3}{4}

Decimal Notation

- 0.75

Solution steps

tan (arccos (- \frac{4}{5}))

Rewrite using trig identities:

tan (arccos (- \frac{4}{5})) = \frac{1 - ( - \frac{4}{5} ) ^{2}}{( - \frac{4}{5} )}

Use the following identity:

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

= \frac{1 - ( - \frac{4}{5} ) ^{2}}{( - \frac{4}{5} )}

= \frac{1 - ( - \frac{4}{5} ) ^{2}}{- \frac{4}{5}}

Simplify

= - \frac{3}{4}

sin (\frac{- π}{3})

sin (\frac{- π}{6})

\frac{sin ( π )}{2}

cos (- 27 0^{\circ})

arcsin (sin (\frac{π}{3}))