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

The value of cot(arcsin(-1/2)) is -sqrt(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

5 cos (\frac{3 π}{2})

cos (11 0^{\circ}) cos (5 0^{\circ}) - sin (11 0^{\circ}) sin (5 0^{\circ})

arccos (9)

arcsin (\frac{6}{11})

12 cos (0)

What is the value of cot(arcsin(-1/2)) ?
The value of cot(arcsin(-1/2)) is -sqrt(3)