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

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loochy | Student | eNoter

Posted June 1, 2011 at 11:34 PM via web

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 1, 2011 at 11:40 PM (Answer #1)

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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

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giorgiana1976 | College Teacher | Valedictorian

Posted June 2, 2011 at 12:00 AM (Answer #2)

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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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