What is the value of cot(arcsin(1/2)) ?

The value of cot(arcsin(1/2)) is square root of 3

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cot(arcsin(1/2))

cot (arcsin (\frac{1}{2}))

3

Decimal Notation

1.73205 \dots

Solution steps

cot (arcsin (\frac{1}{2}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= 3

- 3 sin (π)

200 sin (6 0^{\circ})

sec (0 π)

sec (5 π)

8 sin (6 0^{\circ})

What is the value of cot(arcsin(1/2)) ?
The value of cot(arcsin(1/2)) is square root of 3