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.