Advice 1: How to find the angle knowing the cosine

In addition to direct trigonometric functions sine and cosine, there are and return them to the arc sine and arccosine. They can be used to calculate the angles using the known values of the direct functions. There are several variants of practical implementation of such calculations.
How to find the angle knowing the cosine
Use the inverse cosine (arccosine) to find the angle at the known value of the cosine. The desired value of the arc tangent, and the angle can be found for example in "tables Bradis". Paper copies of this Handbook are available in libraries and bookstores, and e-can be found on the Internet.
Find online online calculator to calculate inverse trigonometric functions and determine with their help the desired value. To use such services much easier than to look up values in tables. In addition, they can simplify the calculations since many of these calculators allow you to compute not only single values but also to the results based on the formulas composed of several operations with the trigonometric functions.
Use the standard calculator Windows, if you want to do without access to the Internet. Start command of the calculator placed in the main menu on the "start" button. Opening it, navigate to "All programs", then to "Standard" and click "Calculator". By default, it starts with the simple interface, not having tools for trigonometric calculations. Open it in menu "View" and select the item labeled "Engineering".
Enter a value for the cosineand from the keyboard, or clicking corresponding buttons of the calculator interface. Can be used to input a copy operation (CTRL + C) and paste (CTRL + V). Then select the units which should be represented the result (degrees, radians, or grads) - the corresponding selector is a line below the input field number. After this it is necessary to mark invert functions in the Inv checkbox. That's all cooking is over, click the cos and the calculator will calculate the value of the inverse cosinefunction (arccosine) of the given value and present the result in the selected units.

Advice 2: How to find the cosine, the sine of knowing

In order to obtain a formula linking the sine and cosine of the angle, it is necessary to give or to recall some definitions. So, the sine of an angle is the ratio (quotient of the) opposite side of a right triangle to the hypotenuse. Tothe sine of an angle is the ratio adjacent side to the hypotenuse.
How to find the cosine, the sine of knowing
Draw a right triangle ABC, where angle ABC is a straight line (Fig.1). Consider the ratio of the sineand cosineand angle CAB. According to the above definition
sin CAB=BC/AC cos CAB=AB/AC.
Remember the Pythagorean theorem - AB^2 + BC^2 = AC^2, where ^2 is the operation of squaring.
Divide left and right side of the equation by the square of the hypotenuse AC. Then the previous equation will look like this:
AB^2/AC^2 + BC^2 AC^2 = 1.
For convenience, we rewrite the equation obtained in step 2, as follows:
(AB/AC)^2 + (BC/AC)^2 = 1.
According to the definitions given in step 1, we get:
cos^2(CAB) + sin^2(CAB) = 1, i.e.
cos(CAB)=SQRT(1-sin^2(CAB)), where SQRT is the operation of taking the square root.
Useful advice
The magnitude of the sine and cosine of any angle cannot be greater than 1.
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