I know the cosine and need to know how to enter it to get the angle. The cosine is .5553, what do I push to find out the angle?

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 cosine of 52 degrees is about .6157 . The inverse cosine of .6157 is 52 degrees.

52 degrees is a measure of an angle. .6157 is a distance. The cosine of an angle results in a distance, while the inverse cosine of a distance results in an angle. There is no such thing as the inverse cosine of an angle, just as there is no such thing as the cosine of a distance. It's like asking "How heavy is one hour?"

If you're asking how to calculate a cosine or inverse cosine on your calculator, please specify the make and model of the calculator.

Nothing's wrong, your calculator is giving you the cosine of 42 radians. If you want the cosine of 42 degrees (which is 0.74314), press MODE, down-arrow to the "Angle" line, press right-arrow, select "2:DEGREE", and press ENTER twice.

To get the angle from a value of the cosine, you use the arc cosine or arcosin function. It is the shifted function of the cosine key. Be careful with the units. If the calculator is configured with the degree angle unit, the value returned by the arc cosine will be in degrees. If the angle unit is the radian, the result will be in radians.

The inverse sine and cosine equations mean "angle who's sine/cosine is:" The bounds of the arguments for these functions must be between 1 and -1, the maximum and minimum values of the sine and cosine functions, because no angle can have a sine or cosine that is greater than 1 or smaller than -1. Also it should be noted that the inverse sine/cosine function is not the same as 1/sine or 1/cosine, although the symbol makes it look like that.

Sinus, cosinus, and tangens (Latin names) are the same as sine, cosine, and tangent (full English names), which are abbreviated to sin, cos, and tan. If you're asking how to use these functions, they deal with right triangles and finding the missing angles or side lengths of the triangle.

Always, sine equals opposite/hypotenuse, cosine equals adjacent/hypotenuse, and tangent equals opposite/adjacent.


Using this picture, the sine of angle A equals a/c, the tangent of angle B equals b/a, and the cosine of angle A equals b/c, and so on.

In a calculator, simply hit the desired function (sin, cos, or tan), then in parenthesis put the measure of the angle, and then use what you know about the triangle to find out the rest.

You are indeed committing an error. The sequence [2nd][COS] is activating the function arcosine or arccos or cos^-1, the inverse of the cosine function. If you remember the properties of the cosine functions, you know that cos(x) is defined over the real line ]- infinity to infinity[, but its range spans the interval [-1,1].
Since the arcosine function is the inverse of the cosine, its domain of definition is the range of the cosine, namely the closed interval [-1,1].

Thus if you enter [2nd][COS][3180.04] the calculator flags this as a domain error, because 3180.04 is outside the interval [-1,1]

Restrict the argument of cos^-1 to any value inside the closed interval [-1,1].
When manipulating the trigonometric functions and their inverses you must keep in mind that the results you get are dependent on the angle unit your calculator is configured for (deg, rad).

Let su rephrase the question, just to be sure we are on the same wavelength. The cosine of an angle is 0.5: What is the value of the angle? Right?.

First of all you must set the angle unit to degree or radian.

1. Press [SHIFT][MODE\ and select the appropriate unit.
2. Press [SHIFT][COS] to access the arc cosine function (COS^-1) enter 0.5, close the right parenthesis and hit [=]
   

If you unit is the degree you should find 60 degrees.
If the angle unit is the radian, the result should be 1.045 radian.

The cosine function takes its value on the whole real line, the angle domain spans ]-infinity, + infinity[. The range of the function is however limited to the [-1, +1] interval.
Thus if you want to calculate the arc (angle) from the value of the cosine, the cosine must be in the interval [-1, +1]. Any value outside this domain will give you a domain error.
Check that the values you feed to the arc cosine function are in the interval [-1,+1].

If the angle unit is the degree the value returned bay [cos^-1] is in degrees, and if the angle unit is the radian, the value returned is in radians

Hello,
I believe you are not pressing the keys in the right order.
If you know how to set angle unit, skip this part and go to Exemples

If you want to calculate the sine , cosine or tangent of an angle given in degrees, the calculator must have the angle unit set to degrees. To do so :Turn calculator ON, scroll to [RUN] icon and press [EXE] then [SHIFT][SETUP]. On the fifth line angle must be set Degrees. If it is not in degrees, press the key correspondig to menu deg (F1)
(If you have to use the Radian as unit of angle, that is where you set it.)
So your angle is in degrees.
Exemples
To calculate the sine of 15 degrees press [SIN] 15 [EXE].
If expression inside the sine is complicated or contains diverse operations use parentheses as in the exemple
[SIN] [(] 90/2 -180/3 [)] [EXE].
You proceed the same way for cosine, or tangent.

Hope it helps.