Calculate the expression sin^-1(sin(5pi/3))+tan^-1(tan(2pi/3))?

Expert Answers
justaguide eNotes educator| Certified Educator

We have to determine the value of sin^-1(sin(5pi/3)) + tan^-1(tan(2pi/3))

sin^-1(sin(5pi/3)) or arc sin (sin (5pi/3)) = 5*pi/3

tan^-1(tan(2pi/3)) or arc tan (tan (2pi/3)) = 2*pi/3

Adding 5*pi/3 and 2*pi/3:

5*pi/3 + 2*pi/3 = 7*pi/3

The result of the expression is 7*pi/3

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.