What is the value of tan(arcsin((sqrt(5))/3)) ?

The value of tan(arcsin((sqrt(5))/3)) is (sqrt(5))/2

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tan(arcsin((sqrt(5))/3))

tan (arcsin (\frac{5}{3}))

\frac{5}{2}

Decimal Notation

1.11803 \dots

Solution steps

tan (arcsin (\frac{5}{3}))

Rewrite using trig identities:

tan (arcsin (\frac{5}{3})) = \frac{( \frac{5}{3} ) 1 - ( \frac{5}{3} ) ^{2}}{1 - ( \frac{5}{3} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{5}{3} ) 1 - ( \frac{5}{3} ) ^{2}}{1 - ( \frac{5}{3} ) ^{2}}

= \frac{\frac{5}{3} 1 - ( \frac{5}{3} ) ^{2}}{1 - ( \frac{5}{3} ) ^{2}}

Simplify

= \frac{5}{2}

sin (2 π + \frac{π}{2})

67 sin (4 5^{\circ})

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

cos (- 3)

sin (9 0^{\circ}) + cos (6 0^{\circ})

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