InterviewSolution
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InterviewSolution
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Find the principal values of the following (i) `sin^(-1) (sin 1)` (ii) `sin^(-1) (sin 2)` (iii) `sin^(-1) (sin 10)` (iv) `sin^(-1) (sin 20)` (v) `sin^(-1) (sin 100)` (vi) `sin^(-1) (sin. (29 pi)/(5))` |
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Answer» (i) Since `1 in [-pi//2, pi//2], sin^(-1) (sin 1) = 1` (ii) Since `2 in [-pi//2, pi//2], sin^(-1) (sin 2) != 2` `:. Sin^(-1) (sin 2) = sin^(-1) (sin (pi) -2))` `= pi - 2 " as " (pi - 2) in [-pi//2, pi//2]` (iii) `sin^(-1) (sin 10) = sin^(-1) (sin (3 pi - 10))` `= 3 pi - 10 " as " (3 pi - 10) in [-pi//2, pi//2]` (iv) `sin^(-1) (sin (-20)) = sin^(-1) (sin (6 pi - 20))` (v) `sin^(-1) (sin 100) = sin^(-1) (sin (100 - 32 pi))` `= 100 - 32 pi " as " (100 - 32 pi) in [-pi//2, pi//2]` (vi) `sin^(-1) (sin.(29 pi)/(5)) = sin^(-1) (sin(6 pi - (pi)/(5)))` `= sin^(-1) (sin(-(pi)/(5)))` `= -(pi)/(5)` |
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