What is the value of tan(arccos(0.9)) ?

The value of tan(arccos(0.9)) is (sqrt(19))/9

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tan(arccos(0.9))

tan (arccos (0.9))

\frac{19}{9}

Decimal Notation

0.48432 \dots

Solution steps

tan (arccos (0.9))

= tan (arccos (\frac{9}{10}))

Rewrite using trig identities:

tan (arccos (\frac{9}{10})) = \frac{1 - ( \frac{9}{10} ) ^{2}}{( \frac{9}{10} )}

Use the following identity:

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

= \frac{1 - ( \frac{9}{10} ) ^{2}}{( \frac{9}{10} )}

= \frac{1 - ( \frac{9}{10} ) ^{2}}{\frac{9}{10}}

Simplify

= \frac{19}{9}

5 cos (2 (125)) + 7

arccos (\frac{3}{35})

2 tan (\frac{2 π}{3})

cot^{2} (2 4^{\circ}) - csc^{2} (2 4^{\circ})

\frac{2}{1 - 2 sin ( 3 0 ^{\circ} )}

What is the value of tan(arccos(0.9)) ?
The value of tan(arccos(0.9)) is (sqrt(19))/9