Asked by terra
using the intermediate value theorum, prove that arctanx = arccosx has a solution.
i've gotten that the domain of arctanx is -pi/2 to pi/2 but i'm not sure where to go from here...can i move the arccosx to the left? when i do that, i can't figure f(pi/2) though..i'm confused!
i've gotten that the domain of arctanx is -pi/2 to pi/2 but i'm not sure where to go from here...can i move the arccosx to the left? when i do that, i can't figure f(pi/2) though..i'm confused!
Answers
Answered by
Steve
on x in [0,1]
arctan rises from 0 to pi/4
arccos falls from pi/2 to 0.
Since both functions are continuous,
arccos - arctan assumes all values between pi/2 and -pi/4
That would include 0, meaning arctan = arccos
arctan rises from 0 to pi/4
arccos falls from pi/2 to 0.
Since both functions are continuous,
arccos - arctan assumes all values between pi/2 and -pi/4
That would include 0, meaning arctan = arccos
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