I'm trying to find the inverse cotangent of -2/3, and whenever I input Tangent^-1 (1/(-2/3)) it gives me .98279, however for homework we are using this software called Hawkes learning Center and it gives me a completely different answer 2.1588. Does anyone know how do figure that out?

the inverse tangent

* (-tan)

The inverse cosine function is defined for arguments from -1 to +1. 6 is outside of this domain, thus the error. Do you get an error if you try the inverse cosine of 0.6, for example?

If you're getting the same error for the inverse tangent, could you post an example?

Not quite true. (Explanation at the end)
The sine and cosine of an angle have values in the closed interval [-1,1]. That means whatever the value of the angle, its sine or its cosine cannot be less than -1 or greater than 1.
When you consider the inverse problem where you want to find the angle whose sine or cosine is known, you must take the values of the sine or cosine in the interval [-1,1]. That is the domain of the functions arc sine and arc cosine. So if you take a value outside the domain [-1,1], and want to calculate the angle to which it belongs, the calculator signals that there a domain error, because there is no angle that answers the question. Limit the arguments of the sin^-1 and cos^-1 to values in [-1,1]
For the inverses of arc tangent and arc cotangent functions there is no domain limitation because the range of tangent and cotangent is the whole real line ]-infinity, +infinity[.

The sine and cosine function have a range between [-1, 1]. The domain of their inverse functions is [-1,1]. So 20/1 which is 20 is out of the domain of definition of the functions. No limitations for tangent and cotangent.

No, you don't need a new calculator. Yours simply has the angular mode set to grads. The inverse tangent of 1 is 50 grads, the inverse tangent of sqrt(3) is 66.6... grads.
To change the angular mode, press MODE one or more times until you get the display "Deg Rad Gra". Select the mode you want (from the results you're expecting, it's 1 for Deg).

If you are trying to calculate arcsine (sin^-1) and arccosine (cos^-1) the only whole number you can use are -1,0 and 1. This due to the fact that the domain of these functions is the closed interval [-1,1]. Any value outside that interval will trigger an error message. No limitation on the argument of the arc tangent or arc cotangent functions

If the angle unit is set to degree the arc will be in degrees, and if angle unit is radian, the arc will be in radians.

There is no Inverse Cotangent on the Calculator, but you have Inverse Tangent.

Cotangent is just the reciprocal of tangent.




Just inverse the fraction and use inverse tangent to get its cotangent. Hope this helps.

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.

By definition

1. cosecant of X =1/sin(X), must not be confused with arc sine [sin^-1]
   
2. secant of X =1/cos(X), must not be confused with arc cosine [cos^-1]
3. 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

1. You enter 1 / [sin] 37 [ ) ] [ENTER] result is 1.661640141
2. 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.*