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

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

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tan(arccos((sqrt(2))/3))

tan (arccos (\frac{2}{3}))

\frac{7}{2}

Decimal Notation

1.87082 \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{7}{2}

10 (cos (3 0^{\circ}))

cot (\frac{2}{3} π)

tan (arctan (\frac{π}{4}))

\frac{1}{sec ^{2} ( 0 + 0 )} - 1

arccos (\frac{70}{100}) \cdot 2

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