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}

sin (arcsin (3))

arctan (\frac{0}{4})

cos (2 \frac{π}{2})

\frac{1 - cos ( 6 0 ^{\circ} )}{2}

cos (- 63 0^{\circ})

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