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symsane
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I could not found any answer to this question: What is sin-1(2i) equal?
The function sin-1(2i) is the inverse sine function, also known as arcsine, applied to the complex number 2i. It represents the angle in radians whose sine is equal to 2i.
No, sin-1(2i) is not a real number because it involves the imaginary number i. It is a complex number with a real part of 0 and an imaginary part of ln(2+√5).
To calculate sin-1(2i), you can use the formula sin-1(z) = ln(iz + √(1-z^2)) where z is the complex number. In this case, z=2i. Plugging in the values, we get sin-1(2i) = ln(2i + √(1-4)) = ln(2i + √(-3)) = ln(2i + i√3).
The principal value of sin-1(2i) is the principal branch of the inverse sine function, which is defined for complex numbers with a magnitude less than or equal to 1. Since 2i has a magnitude greater than 1, sin-1(2i) does not have a principal value.
The range of values for sin-1(2i) is the set of all complex numbers, since the inverse sine function is defined for all complex numbers. However, as mentioned before, the principal value does not exist for this particular input. It is important to note that the range of values for inverse trigonometric functions may vary depending on the definition and conventions used.