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Find sin^-1(sin 5pi/2)+tan^-1(tan 2pi/3)?

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leaffyblue | Student, College Freshman | eNoter

Posted December 3, 2011 at 11:55 PM via web

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Find sin^-1(sin 5pi/2)+tan^-1(tan 2pi/3)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted December 4, 2011 at 12:19 AM (Answer #1)

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Calculate`sin 5pi/2 = sin(4pi/2 + pi/2) = sin (2pi + pi/2) = sin pi/2 = 1`

Calculate `tan 2pi/3 = tan (pi/3 + pi/3) = (tan (pi/3) + tan (pi/3))/(1 - tan^2 (pi/3))`

`` `tan 2pi/3 = (2 tan (pi/3))/(1 - tan^2 (pi/3))`

`tan 2pi/3 = (2 sqrt 3)/(1 - 3) = (2 sqrt3)/(-2) = -sqrt3`

`` Use the notation `sin^-1 alpha = arcsin alpha =gt sin^-1 5pi/2 = arcsin 5pi/2 = arcsin 1`

Use the notation `tan^-1 alpha = arctan alpha =gt tan^-1 2pi/3 = arctan 2pi/3 = arctan (-sqrt 3)`

`arcsin 5pi/2 + arctan 2pi/3 = arcsin 1 + arctan (-sqrt 3) = pi/2 - pi/3 = pi/6`

The value of sum the inverse trigonometric functions is `arcsin 5pi/2 + arctan 2pi/3 = pi/6.`

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