Calculate the expression sin^-1(sin(5pi/3))+tan^-1(tan(2pi/3))?
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We have to determine the value of sin^-1(sin(5pi/3)) + tan^-1(tan(2pi/3))
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giorgiana1976 | Student
We'll solve the problem based on the following rules:
sin^-1(sin(x)) = arcsin (sin x) = x and arctan(tan x) = x
tan^-1(tan(x)) = arctan(tan x) = x
According to these rules, we'll get:
arcsin (sin (5pi/3)) = 5pi/3
arctan(tan (2pi/3)) = 2pi/3
arcsin (sin (5pi/3)) + arctan(tan (2pi/3)) = 5pi/3 + 2pi/3
arcsin (sin (5pi/3)) + arctan(tan (2pi/3)) = 7pi/3
The values of the given sum of inverse trigonometric functions is 7pi/3.
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