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What is cot parenthesis sin to the negativde 1 parenthesis 2 over 3 closed parenthesis and another closed parenthesis?
Kiwi215
If I read that correctly, you have:
cot(sin-1(2/3))
which I understand to mean
cot(arcsin(2/3))
which has the value
1/2 x √5
sin(arcsin(x)) = x
cos2θ + sin2θ = 1
⇒ cosθ = √(1 - sin2θ)
cotθ = cosθ ÷ sinθ
⇒ cot(arcsin(2/3)) = cos(arcsin(2/3)) ÷ sin(arcsin(2/3)
= √(1 - sin2(arcsin(2/3))) ÷ sin(arcsin(2/3)
= √(1 - (2/3)2) ÷ (2/3)
= 1/3 x √(9 - 4) x 3/2
= 1/2 x √5
As the reciprocal trignometric functions have separate names, eg 1/tan x = cot x, the use of the -1 "power" to indicate the inverse function is possible. However, to avoid any possible confusion, I prefer to use the arc- prefix to indicate the inverse function.
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∙ 12y ago
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