Commonly used functions and cofunctions are as follows:

    sin A = cos (90 A)

    sec A = csc (90 A)

    tan A = cot (90 A)

FUNCTIONS OF OBTUSE ANGLES

In figure 1-22, the point P has generated an obtuse (larger than 90) angle of 135. This angle is the supplement of 45 (two angles are supplementary when they total 180). We have left a dotted image of the reference angle A, which is equal to the supplementary angle of 135. You

can see that the values of x, y, and r are the same for 135 as they are for 45, except that the value of x is negative. From this it follows that the functions of any obtuse angle are the same as the functions of its supplement, except that any function in which x appears has the opposite sign.

The sine of an angle is y/r. Since x does not appear in this function, it follows that sin A = sin (180 A). The cosine of an angle is fir. Since x appears in this function, it follows that cos A = - cos (180 A). The tangent of an angle is y/x. Since x appears in this function, it follows that tan A = tan ( 180- A). The importance of knowing this lies in the fact that many tables of trigonometric functions list the functions only for angles to a maximum of 90. Many oblique triangles, however, contain angles larger than 90. To determine a function of an angle larger than 90 from a table that stops at 90, you lookup the function of the supplement of the angle. If the function is a sine, you use it as is. If it is a cosine or tangent, you give it a negative sign.

The relationships of the function of obtuse angles are as follows:

The above relationships apply only when angle A is greater than 90 and less than 180.