When is cotangent undefined

Hence, is undefined when or. All negative numbers and 0. All positive numbers and 0. All real numbers except 0. The domain of a function is the range of all possible inputs, or x-values, that yield a real value for f x. Trigonometric functions are undefined when they represent fractions with denominators equal to zero. In any triangle created by the angle x and the x-axis, the hypotenuse is a nonzero number. Which of the following trigonometric functions is undefined?

The value of tan pi is 0, so the cotangent of pi must be undefined. The value of tan 0 is 0, so the cotangent of 0 must be undefined.

The value of sin 0 is 0, so the cosecant of 0 must be undefined. In a triangle created by the angle x and the x-axis, the adjacent side length lies along the x-axis; however, when the angle x lies on the y-axis, no length can be drawn along the x-axis to represent the angle. The value of sin pi is 0, so the cosecant of pi must be undefined. If you've found an issue with this question, please let us know.

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Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Hanley Rd, Suite St. Louis, MO The cotangent function is like a mirror image of the tangent function, phase shifted ninety degrees left or right. It falls from its positive peak as it moves away from zero degrees to a value of zero at ninety degrees , and then falls again to its negative peak as it approaches one hundred and eighty degrees.

It then transitions to its positive peak and repeats the cycle again. As with the other trigonometric functions we have looked at, we don't need to use tables to find the cotangent of an angle or the angle corresponding to a given cotangent value , since any modern scientific calculator can do it for us, even though most calculators don't have a dedicated button for the cotangent function.

Finding the cotangent of an angle with the built-in calculator provided in Microsoft Windows is still relatively straightforward. The scientific version of the calculator can be selected from the application's View menu. To find the cotangent of forty-eight degrees using the Windows calculator, enter the following keystrokes if you don't have the Windows calculator, use any available calculator that can perform trig functions :.

Make sure, by the way, that you have the calculator set to the Degrees mode unless you are planning to enter a value for the angle in radians or gradians. If you have entered the keystrokes correctly, you should now see the following display:. So far, so good. Now let's assume that you want to find the size of an acute angle in a right-angled triangle by first finding the quotient of the adjacent and opposite i. Providing you have values for the lengths of the sides of the triangle, you can find the value of the angle's cotangent easily enough.

Finding the angle is not quite as straightforward as for the three main trigonometric functions, as most calculators do not have a dedicated button for the arccotangent function which is the inverse of the cotangent function.

Fortunately, there is a relatively simple way around that. We can actually find the size of the angle in a single operation on the Windows calculator. We do this by using brackets in the key sequence entered, in order to get the calculator to find the inverse of the quotient of the adjacent and opposite i.

We then apply the arctangent function to the result. Here is the key sequence to use:. You may have already worked out that what we did here was to find the tangent of the angle by taking the reciprocal of the cotangent. We then simply applied the arctangent function to the result. It is also known as the log function of infinity to the base e. Cotangent is not same as tangent inverse. Cotangent function is equal to the reciprocal of tangent function.

What is arcsin? Arcsine is the inverse of sine function. It is used to evaluate the angle whose sine value is equal to the ratio of its opposite side and hypotenuse. The inverse of the cotangent function is called inverse cotangent or arccot. It is denoted by cot — 1 x. Save my name, email, and website in this browser for the next time I comment.

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