What is the value of tan(arccos(1/3)) ?

The value of tan(arccos(1/3)) is 2sqrt(2)

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tan(arccos(1/3))

tan (arccos (\frac{1}{3}))

22

Decimal Notation

2.82842 \dots

Solution steps

tan (arccos (\frac{1}{3}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= 22

cot (0 π)

10 \cdot sin (4 5^{\circ})

sec (\frac{1}{2})

sin (- \frac{3}{5})

1 - 2 sin^{2} (22. 5^{\circ})

What is the value of tan(arccos(1/3)) ?
The value of tan(arccos(1/3)) is 2sqrt(2)