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^{2} (12 0^{\circ}) + cos^{2} (12 0^{\circ})

2 sin^{2} (x) = 1

sin (2 x) = sin (x)

cos (4 5^{\circ})

arctan (- \frac{1}{3})

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