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To calculate the cotangent of an angle, calculate the angle's tangent and then take the reciprocal.
To calculate the angle given a cotangent, take the tangent's reciprocal then the arctangent.
If you're asking how to do this on a particular calculator, what make and model?
The tangent function (and the cotangent) are periodic, with a period of pi. The calculator will give you a result from -pi/2 to pi/2, while the Hawkes apparently is giving you a result from 0 to pi. The difference between 2.1588 and -.98279 is pi.
To make the calculator's result match Hawkes, if the (co)tangent gives you a negative value, simply add pi to it.
The cotangent function is not implemented on the TI84PLUS native OS and consequently you will not find its inverse function on the calculator. However, there exits an equivalence (definition) between arc cotangent(x) and arc tangent (1/x). Thus cot^(-1)(X)= tan^(-1)(1/X),
Be careful. Since it is a multivariate function, some authors define the principal branch in the domain [0, PI], while others define the domain on [-Pi/2, Pi/2]. You will have to consult your textbook, or the documents you are using to find out the domain of the principal branch.
cosecant of X =1/sin(X), must not be confused with arc sine [sin^-1]
secant of X =1/cos(X), must not be confused with arc cosine [cos^-1]
cotangent of X =1/tan(X), must not be confused with arc tangent [tan^-1]
Because of these simple relations, calculator makers do not implement them with specific key sequences. On this calculator, you have two ways to calculate one of these functions. EX cosecant of 37 degrees
You enter 1 / [sin] 37 [ ) ] [ENTER] result is 1.661640141
You enter [sin] [ ) ] 37 [ENTER] followed by [X^-1] to take the reciprocal of the previous answer. The [X^-1] key is the one just below [MATH].
A word of caution: secant cosecant and cotangent must not be confused with the inverse trigonometric functions arcsin, arccos, arctan
because cotangent, cosecant, and secant are all inverse trig functions, just type in 1 / |shift| trig function and the number if you are finding the angles. It might not be a dedicated button, but its an extra push, and it will give you the same result. *note that I put the shift press only because that is how you get the inverse tan to get an angle from a tan ratio.*
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