What is the value of tan(arccos(-3/7)) ?

The value of tan(arccos(-3/7)) is -(2sqrt(10))/3

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tan(arccos(-3/7))

tan (arccos (- \frac{3}{7}))

- \frac{2 10}{3}

Decimal Notation

- 2.10818 \dots

Solution steps

tan (arccos (- \frac{3}{7}))

Rewrite using trig identities:

tan (arccos (- \frac{3}{7})) = \frac{1 - ( - \frac{3}{7} ) ^{2}}{( - \frac{3}{7} )}

Use the following identity:

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

= \frac{1 - ( - \frac{3}{7} ) ^{2}}{( - \frac{3}{7} )}

= \frac{1 - ( - \frac{3}{7} ) ^{2}}{- \frac{3}{7}}

Simplify

= - \frac{2 10}{3}

1 - cos (3 0^{\circ})

sin (0.34)

- cos (\frac{4 π}{3}) + cos (\frac{2 π}{3})

sec^{2} (\frac{7 π}{6})

sin (7 \frac{π}{2})

What is the value of tan(arccos(-3/7)) ?
The value of tan(arccos(-3/7)) is -(2sqrt(10))/3