How do you find the domain of f(x) = tan(3arccos(x))?

1 Answer
MattyMatty
Dec 15, 2017

"By combining domain of arccos(x) and tan(x), see explanation:"
[-1, 1] " \ {"-sqrt(3)/2", 0, "+sqrt(3)/2" }"

Explanation:

"arccos(x) is defined only for x "in" [-1, 1]."
"tan(x) is defined for all x values, except "pi/2 + k pi" , k integer."
"So we check : "
"3 arccos(x) = "pi/2 + k pi"."
=> arccos(x) = pi/6 + k pi/3"
=> x = cos(pi/6 + k pi/3)"
=> x = pm sqrt(3)/2, or 0
"For those 3 x-values, the function f(x) is not defined, so we have"
"as domain :"
[-1, 1] " \ {"-sqrt(3)/2", 0, "+sqrt(3)/2" }"

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