## Precalculus Test Out Practice Exam

Part 4 Test 1 Time: 3 hours

1. Find the exact solution(s) to the equation

Answer: There is no solution because x=3 is not in the domain of the original equation.

2. If , find .

3. Write the following trigonometric expression as an algebraic expression in x:

4. Find two angles that have the point (-3,7) on the terminal side of the angle.

Answer: The two angles are , and .

5. Building A and Building B are 100 feet apart. If the angle of depression from the top of Building A to the top of Building B is 10 degrees, how much taller is Building A than Building B?

Answer: Building A is 17.6 feet higher than Building B.

6. Find the exact value of

Answer: The exact value is 1.

7. Concerning the following function

• What is the period of the function?

Answer: The period of the function f(x) is .

• What is the amplitude of the function?

Answer: The amplitude of the function f(x) is 3.

• What is the maximum value of the function?

Answer: The maximum value of the function f(x) is 14.

8. Where do the graphs of the functions , and intersect on the interval [6,14]?

Answer: The are two points of intersection which are approximately (9.032,7.791) and (9.605,7.027).

9. Find the approximate range of the function

Answer: The range of the function f(x) is approximately [-2.889,2.889].

10. The graph of the function

is bounded by two graphs. What are the equations of the boundary graphs?

Answer: The graph of the function is bounded above by the line , and below by the line .

11. What is the phase shift of the graph of

Answer: The phase shift of the graph is .

12. Restrict the domain of the function so that its inverse exists.

Answer: The restricted domain is . There are many other solutions, e.g. .

13. Find .

Answer: The expression is not defined, since the domain of the function is [-1,1], and 2 does not lie in this interval.

14. If point A is located at (2,3) and point B is located at (-8,14), give the bearing and distance from point A to point B.

Answer: The bearing from point A to point B is . The distance from point A to point B is .

15. In triangle ABC, angle equals 40 degrees, angle equals 30 degrees, and side AB equals 10 inches. Find the exact value of side AC.

Answer: The exact value of side AC is

16. Convert 150 radians to degrees in the degree-minute-second format.

17. Find the equation of the circle that passes through the points (2,3), (7,1), (9,5).

Answer: The equation of the circle is

18. If , and the terminal side of t is located on the second quadrant, find .

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Wed Jul 16 15:55:54 MDT 1997