Make the given changes in the indicated examples of this section and then find the indicated values.

In Example 2, interchange a and b and then find the values.

Data from Example 2

Given a = 4, b = 7, and c = √65 (see Fig. 4.33), find sin A, cos A, tan A, sin B, cos B, and tan B in exact form and in approximate decimal form (to three significant digits).

We see that A and B are complementary angles. Comparing values of the functions of angles A and B, we see that sin A = cos B and cos A = sinB.

sin A = cos A = tan A = side opposite angle A hypotenuse side adjacent angle A hypotenuse side opposite angle A side adjacent angle A = II 65 65 # = 0.496 sin B = = 0.868 cos B = = 0.571 tan B = side opposite angle B hypotenuse side adjacent angle B hypotenuse side opposite angle B side adjacent angle B || || || = 7 65 74 = 0.868 = 0.496 = 1.75