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sin(-1sin(1.325))

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3 Answers

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.

I'm making a few assumptions here:  

1.  Your problem is Inverse Sine of 1.325 radians (not degrees)

2.  By Inverse Sine you also mean Sine-1 or ArcSin

A trig (Trigonometry) table gives ArcSin(1.325 radians) = 14.07°, or x = 0.970