Exercises for Chapter 3 Sections 3 and 4.

In all of the following problems give trigonometric functions to 4 decimal places, find all angles in the same units as angles given in the problem with 1 decimal place for degrees and 3 decimal places for radians, and give all lengths with the same number of decimal places as lengths given in the problem.
 

1. Find the six trigonometric functions for 
 

2. Find the six trigonometric functions for 
 

3. Find the six trigonometric functions for 
 

4. Give each of the following in degrees:

(a) Arcsin(0.7739);         (b) Arcsin(-0.7739);         (c) Arccos(0.7739);         (d) Arccos(-0.7739);

(e) Arctan(0.7739);         (f) Arctan(-0.7739).
 

5. Find an angle in radians whose secant is 2.4483.
 

6. Graph  on the same plot on the calculator.
 

7. Solve each of the following triangles (See Figure 3c) from the given information if possible.

(a) b = 39.47;

(b) a = 2.917, c = 3.264;

(c) a = 472.6, b = 515.1, c = 497.7, find angles in radians.
 

8. Reconsider Calculator Example 3.4.2.

(a) After finding c, use the Law of Sines and the ASIN function to find  was found in the example.

(b) Why do you get a different answer for  than what was found in the example and what must be done to insure this error does not occur?

9. Solve each of the following triangles:

(a) b = 29.52, c = 12.77;

(b) a = 2.932, c = 5.761;

(c)  radians, a = 139.7, b = 62.4.
 

10. Show that if you are given two angles and a side which is not the included side, (AAS or SAA), the triangle is still determined. This is usually a corollary to the ASA theorem.
 

11. Why is AAA not a congruence theorem?
 

12. Show that SSA does not determine a triangle by finding two distinct triangles which satisfy a = 2.41, b = 4.07,