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.

Instruction

1. 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.
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.
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.