What is the value of cot(arcsin(1/4)) ?

The value of cot(arcsin(1/4)) is square root of 15

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cot(arcsin(1/4))

cot (arcsin (\frac{1}{4}))

15

Decimal Notation

3.87298 \dots

Solution steps

cot (arcsin (\frac{1}{4}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= 15

\frac{sin ( 24 0 ^{\circ} )}{cos ( 12 0 ^{\circ} )}

5 + 4 cos (\frac{π}{2})

(sin (3 0^{\circ})) (tan (4 5^{\circ})) + (tan (3 0^{\circ})) (sin (6 0^{\circ}))

cos (arctan (\frac{5}{12}) + arcsin (\frac{4}{5}))

cos (2 arccos (0))

What is the value of cot(arcsin(1/4)) ?
The value of cot(arcsin(1/4)) is square root of 15