domain and range of inverse trig functions We can get the domain of all inverse trigonometric functions Domain of sin 1 x 1 1 Domain of cos 1 x 1 1 Domain of csc 1 x 1 or 1 Domain of sec 1 x 1 or 1 Domain of tan 1 x All Real Numbers Domain of cot 1 x All Real Numbers Rule to Find Range of Inverse Trigonometric Functions
Then we just interchange the domain and range of trig functions to get the domain and range of inverse trig functions What is the Domain and Range of Sec Theta The domain of sec is R 2n 1 2 and the range is 1 U 1 where n is an integer 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
domain and range of inverse trig functions
domain and range of inverse trig functions
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What is the Range and Domain of Inverse Cosine Trigonometric Function The inverse cosine function is written as cos 1 x or arccos x Inverse functions swap x and y values thus the range of inverse cosine is 0 to pi and the domain is 1 to 1 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
To find the domain and range of inverse trigonometric functions switch the domain and range of the original domain restricted functions Figure PageIndex 1c The inverse sine inverse cosine and inverse tangent 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
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To find the domain and range of inverse trigonometric functions switch the domain and range of the original functions Each graph of the inverse trigonometric function is a reflection of the graph of the original function about the line y x y x Inverse trigonometric functions Domain range of inverse tangent function Google Classroom Microsoft Teams About Transcript Sal finds the formula for the inverse function of g x tan x 3 2 6 and then determines the domain of that inverse function Created by Sal Khan Questions Tips Thanks Want to join the conversation Log in
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