# What is sine-cosine tangent

## Elementary relationships between sine, cosine and tangent and special angles

Here you can find out what relationships exist between the angles in a right triangle and how you can use them to calculate other sizes of the triangle.

### Elementary relationships between sine and cosine

In a right triangle ABC with the right angle at point C, the following applies:

Memorandum 1:

Memorandum 2:

The opposite side of the angle α is the side of the angle β. From the inside angle sum in the triangle (°) follows for a right-angled triangle with °: So: and thus: andThis also applies if you swap α and β. Of course, you can also use the calculator. You calculate the sine of and then use the key:

### sin² (α) + cos² (α) = 1

There is another important relationship between the sine and cosine of an angle:

Memorandum 3:

For every acute angle α the following applies: (where and)

This can be quickly derived from a right-angled triangle:Pythagorean theorem: Choose any angle α and check equality with your calculator. With the help of this relationship you can determine the sine from the cosine or the cosine from the sine for any angle without a calculator.

If so, you switch to: So:

### The tangent as the quotient of sine and cosine

Memorandum 4:

In a right triangle ABC with "the following applies:

If so, then .you replace in with

### The tangent, sine and cosine of 45 °, 30 ° and 60 °

For some angles there are values for sine, cosine and tangent that you can easily remember.

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