Instruction

1

Use the inverse

**cosine**(arc**cosine**) 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.2

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.

3

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".

4

Enter a value for

**the cosine**and 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**cosine**function (arc**cosine**) 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 co**sine**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. To**the sine**of an angle is the ratio adjacent side to the hypotenuse.Instruction

1

Draw a right triangle ABC, where angle ABC is a straight line (Fig.1). Consider the ratio of

sin CAB=BC/AC cos CAB=AB/AC.

**the sine**and co**sine**and angle CAB. According to the above definitionsin CAB=BC/AC cos CAB=AB/AC.

2

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.

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.

3

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.

(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.