What is the value of tan(arcsin(3/4)) ?

The value of tan(arcsin(3/4)) is (3sqrt(7))/7

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tan(arcsin(3/4))

tan (arcsin (\frac{3}{4}))

\frac{3 7}{7}

Decimal Notation

1.13389 \dots

Solution steps

tan (arcsin (\frac{3}{4}))

Rewrite using trig identities:

tan (arcsin (\frac{3}{4})) = \frac{( \frac{3}{4} ) 1 - ( \frac{3}{4} ) ^{2}}{1 - ( \frac{3}{4} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{3}{4} ) 1 - ( \frac{3}{4} ) ^{2}}{1 - ( \frac{3}{4} ) ^{2}}

= \frac{\frac{3}{4} 1 - ( \frac{3}{4} ) ^{2}}{1 - ( \frac{3}{4} ) ^{2}}

Simplify

= \frac{3 7}{7}

arccos (\frac{3}{5.2})

sin (\frac{1}{6})

sec^{2} (5)

sec (arcsin (- \frac{1}{4}))

arccos (\frac{2}{3})

What is the value of tan(arcsin(3/4)) ?
The value of tan(arcsin(3/4)) is (3sqrt(7))/7