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# sin(-1sin(1.325))

sine of the inverse sine of 1.325

### 3 Answers by Expert Tutors

Marc S. | Polymath tutoring math, science, and writingPolymath tutoring math, science, and wri...
4.9 4.9 (703 lesson ratings) (703)
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This is a domain question in disguise. Most high school and college math textbooks introducing inverse trigonometric functions would indicate that the value of sin(sin−1(1.325)) does not exist because sin−1(1.325) doesn't exist.

The sine of any real angle must fall between −1 and 1. This means that the inverse sine function is only permitted to have values between −1 and 1 as its input. Using math vocabulary, the domain of the inverse sine function within the real numbers is [−1,1]. Trying to find sin−1(1.325) within the real numbers is like trying to find √−1 within the real numbers. It doesn't exist because you need a complex number to express the answer.

Of course, if your class is at a more advanced level and is covering the trigonometry of complex numbers then it actually is true that sin(sin−1(1.325)) = 1.325 within complex numbers, but then the question wouldn't be a domain question in disguise.

Carlos D. | Math and Spanish Tutor who caresMath and Spanish Tutor who cares
4.4 4.4 (91 lesson ratings) (91)
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Wrong answer.  Sine and inverse sine are  "inverse" functions so they cancel each other...

Sorry for the correction,   Carlos

Thanks Carlos!

Bill F. | Experienced Teacher & Tutor in Round Rock, TXExperienced Teacher & Tutor in Round Roc...
5.0 5.0 (1 lesson ratings) (1)
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I'm making a few assumptions here: