What is the value of cot(arcsin((sqrt(3))/2)) ?

The value of cot(arcsin((sqrt(3))/2)) is (sqrt(3))/3

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cot(arcsin((sqrt(3))/2))

cot (arcsin (\frac{3}{2}))

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

cot (arcsin (\frac{3}{2}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{3}{3}

cos (108 0^{\circ})

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

arcsec (- 7)

cot (\frac{10 π}{3})

tan (18 0^{\circ}) - 2 cos (18 0^{\circ}) + 3 csc (27 0^{\circ}) + sin (9 0^{\circ})

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