What is the value of tan(arcsin(-5/13)) ?

The value of tan(arcsin(-5/13)) is -5/12

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tan(arcsin(-5/13))

tan (arcsin (- \frac{5}{13}))

- \frac{5}{12}

Decimal Notation

- 0.41666 \dots

Solution steps

tan (arcsin (- \frac{5}{13}))

Rewrite using trig identities:

tan (arcsin (- \frac{5}{13})) = \frac{( - \frac{5}{13} ) 1 - ( - \frac{5}{13} ) ^{2}}{1 - ( - \frac{5}{13} ) ^{2}}

Use the following identity:

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

= \frac{( - \frac{5}{13} ) 1 - ( - \frac{5}{13} ) ^{2}}{1 - ( - \frac{5}{13} ) ^{2}}

= \frac{( - \frac{5}{13} ) 1 - ( - \frac{5}{13} ) ^{2}}{1 - ( - \frac{5}{13} ) ^{2}}

Simplify

= - \frac{5}{12}

sin (2 arcsin (- \frac{1}{2}))

[3 (cos (\frac{π}{12}) + sin (\frac{π}{12}))]^{3}

π - sin (π)

arctan (- 0.75)

3 cos (2)

What is the value of tan(arcsin(-5/13)) ?
The value of tan(arcsin(-5/13)) is -5/12