where is tangent undefined As a result tangent is undefined whenever cos 0 which occurs at odd multiples of 90 and is 0 whenever sin 0 which occurs when is an integer multiple of 180 The other commonly used angles are 30 45 60 and their respective multiples
In other words the tangent function is undefined when is equal to any of these values when is equal to over two plus any integer multiple of We should recall that these values of correspond to the positions of the vertical asymptotes on the graph of tan Where is the tangent function undefined Short Answer Expert verified Answer The tangent function is undefined when 2n 1 2 for any integer n Step by step solution 01 Recall the cosine function properties The cosine function cos has a range of values between 1 and 1
where is tangent undefined
where is tangent undefined
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The tangent being a fraction will be undefined wherever its denominator that is the value of the cosine for that angle measure is zero And thinking back to when you learned about graphing rational functions you know that a zero in the denominator of a function means you ll have a vertical asymptote Whenever cos 0 the function becomes undefined because division by zero is not possible in real numbers These points of undefined values occur at 2 n 1 2 for any integer n leading to vertical lines called asymptotes on the graph of the tangent function
Since tan x sin x cos x the tangent function is undefined when cos x 0 Therefore the tangent function has a vertical asymptote whenever cos x 0 How is the tangent function defined in terms of the sine and cosine functions Why is the graph of the tangent function so different from the graphs of the sine and cosine functions What are important applications of the tangent function
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N e d To graph the tangent function we mark the angle along the horizontal x axis and for each angle we put the tangent of that angle on the vertical y axis The result as seen above is rather jagged curve that goes to positive infinity in one direction and negative infinity in the other The tangent function is defined by 1 where is the sine function and is the cosine function The notation is sometimes also used Gradshteyn and Ryzhik 2000 p xxix
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where is tangent undefined - How is the tangent function defined in terms of the sine and cosine functions Why is the graph of the tangent function so different from the graphs of the sine and cosine functions What are important applications of the tangent function