What is the value of tan(arccos(7/11)) ?

The value of tan(arccos(7/11)) is (6sqrt(2))/7

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tan(arccos(7/11))

tan (arccos (\frac{7}{11}))

\frac{6 2}{7}

Decimal Notation

1.21218 \dots

Solution steps

tan (arccos (\frac{7}{11}))

Rewrite using trig identities:

tan (arccos (\frac{7}{11})) = \frac{1 - ( \frac{7}{11} ) ^{2}}{( \frac{7}{11} )}

Use the following identity:

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

= \frac{1 - ( \frac{7}{11} ) ^{2}}{( \frac{7}{11} )}

= \frac{1 - ( \frac{7}{11} ) ^{2}}{\frac{7}{11}}

Simplify

= \frac{6 2}{7}

sec (arctan (\frac{3 2}{2}))

\frac{10 0 ^{2} ( 2 sin ( 3 0 ^{\circ} ) )}{9.8} - 999.984741

\frac{sin ( 8 0 ^{\circ} ) + sin ( 2 0 ^{\circ} )}{cos ( 8 0 ^{\circ} ) + cos ( 2 0 ^{\circ} )}

8 cos (\frac{π}{2} + 0.1)

ln (2 + tan (\frac{3 π}{32}))

What is the value of tan(arccos(7/11)) ?
The value of tan(arccos(7/11)) is (6sqrt(2))/7