**MACHINE SHOP CALCULATION - OD1640 - LESSON 2/TASK 3**

c.

The trigonometric functions discussed here will be limited to the

sine, cosine, tangent, and cotangent, since practically every common shop

problem in trigonometry can be solved by means of these functions.

The

values of the trigonometric functions in terms of the names of the sides

should be learned. To assist in learning these functions, use the example

below.

EXAMPLE

Using the lettered and named sides of the triangle (figure 12 on the

previous page), write the ratios for sin A, cos A, tan A, cot A, sin B, cos

B, tan B, and cot B.

sin A = a/c; cos A = b/c; sin B = b/c;

cos B = a/c; and tan A = a/b; cot A = b/a;

tan B = b/a; cot B = a/b.

Therefore

sin A = cos B and cos A = sin B

tan A = cot B and cot A = tan B

d.

A trigonometric function expresses the value of an angle in terms of

the sides of the right triangle containing that angle.

For instance, the

value of angle A in figure 13 on the following page may be expressed as:

Thus, if the function and the dimension of one of the sides of that function

ratio are known, then the dimension of the other side can be found.

**52**