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Restrictions For Inverse Trig Functions
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Inverse trig functions do the opposite of the regular trig functions For example Inverse sine sin 1 does the opposite of the sine Inverse cosine cos 1 does the opposite of the cosine Inverse tangent tan 1 does the opposite of the tangent
So to make sure we get a single value out of the inverse trig cosine function we use the following restrictions on inverse cosine theta cos 1 left x right hspace 0 25in hspace 0 25in 1 le x le 1 hspace 0 25in rm and hspace 0 25in 0 le theta le pi
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13 4 Inverses Of Trigonometric Functions YouTube
13 4 Inverses Of Trigonometric Functions YouTube
Since none of the six trigonometric functions are one to one they must be restricted in order to have inverse functions Therefore the result ranges of the inverse functions are proper i e strict subsets of the domains of the original functions
To overcome the problem of having multiple values map to the same angle for the inverse sine function we will restrict our domain before finding the inverse The domain and ranges of the basic inverse trigonometric functions are as follows
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Inverse Trigonometric Values
Inverse Trigonometric Values
9 years ago The restrictions for the inverse function of tan the arctan are quadrants 1 and 4 These restrictions do not apply to the original tan function Since the question stated tan x 1 assuming that the value of x is restricted to pi
In order to define the inverse functions we have to restrict the domain of the original functions to an interval where they are invertible These domains determine the range of the inverse functions The value from the appropriate range that an inverse function returns is called the principal value of the function
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https://tutorial.math.lamar.edu/.../InverseTrig.aspx
So to make sure we get a single value out of the inverse trig cosine function we use the following restrictions on inverse cosine theta cos 1 left x right hspace 0 25in hspace 0 25in 1 le x le 1 hspace 0 25in rm and hspace 0 25in 0 le theta le pi
https://math.libretexts.org/Bookshelves/Precalculus...
The domain of an inverse function is the range of the original function and the range of an inverse function is the domain of the original function Because the trigonometric functions are not one to one on their natural domains inverse trigonometric functions are defined for restricted domains
So to make sure we get a single value out of the inverse trig cosine function we use the following restrictions on inverse cosine theta cos 1 left x right hspace 0 25in hspace 0 25in 1 le x le 1 hspace 0 25in rm and hspace 0 25in 0 le theta le pi
The domain of an inverse function is the range of the original function and the range of an inverse function is the domain of the original function Because the trigonometric functions are not one to one on their natural domains inverse trigonometric functions are defined for restricted domains
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