Test 1: Chapters 1 - 4
Be able to provide written explanation of the process used to find each answer in addition to providing the answer.
1. Convert angle measures using the calculator and paper and pencil (formula) techniques:
600 degrees to radians
60 degrees to radians
pi/4 radians to degrees
3pi/2 radians to degrees
2. Find the length of an arc intercepted by an angle of pi/3 radians on a circle with a 10 inch radius.
3. Find the area of a sector of a circle: Find the area of a slice of pizza if the pizza is 14 inches in diameter and the pizza is cut into 8 equal slices.
4. Find the angular velocity in radians per minute of a 33 1/3 rpm record.
5. Find the linear speed of a needle relative to a record at the time the needle is 10 inches from the center of the record if the record is spinning at 33 1/3 rpm.
6. How fast will a bicycle travel on a bicycle with 26 inch diameter wheels if the rider is pedaling at 60 rpm, the front sprocket has 42 teeth, and the rear sprocket has 14 teeth?
7. Be able to determine all six trig functions EXACTLY for the angles 0, 30, 45, 60, 90, all in degrees.
8. Find all six trig functions to four decimal places for an angle in standard position on a Cartesian Coordinate system where its terminal side goes through the point (3,4).
9. Find all six trig functions to four decimal places for an angle in standard position on a Cartesian Coordinate system which measures 320 degrees.
10. Find all six trig functions to four decimal places for an angle in standard position on a Cartesian Coordinate system which measures 3pi/2 radians.
11. Find the height of a pole vertical to the ground if you measure an angle of 42 degrees from the ground to the top of the pole at a point 20 feet from the base of the pole.
12. Find the length of a guy wire to support a vertical pole if it is attached to the top of a 40 foot high pole and is to make an angle of 57 degrees with the ground.
13. If a circle has a radius of 15 inches, find the length of a chord determined by a 50 degree central angle.
14. If you are sitting 20 feet up in a tree stand and see a deer at an angle of depression of 42 degrees, how far is the deer from the base of the tree? How far is the deer from you? Assume the tree is vertical.
15. Solve the right triangle ABC if a = 12 and angle B is 41 degrees.
16. A surveyor on a mountain road 560 feet above a lake measured the angle af depression to the near and far sides of the lake and found them to be 70 degrees and 23 degrees respectively. Find the distance across the lake.
17. Two observers on the ground 2 miles apart measure the angle of elevation to a hot air balloon which is between them at the same time. The first finds the angle of elevation to be 51 degrees and the second finds the angle to be 32 degrees. Find the height of the balloon above the ground in feet.
18. Sketch the graphs of sin x, cos x, and tan x from -2pi to 2pi.
19. Sketch the graphs of sec x, csc x, and ctn x from -2pi to 2pi.
20. Given a general form of a trig function (eg. y = a sin(bx + c) + d), be able to explain the effect of changing the values of a, b, c, and d. Be able to sketch the resulting graph.
21. Given a graph of a trig function, be able to determine values for a, b, c, and d which will allow you to write a function in the form y = a sin(bx + c) + d, for any of the appropriate three basic functions, which will produce the graph (as in section 3.6 of the text.)
22. Be able to determine if a graph is a graph of a function.
23. Be able to sketch the inverse function or the inverse relation for a given equation or graph.
24. Be able to identify the domain and range for a relation.
25. Be able to express a relation in parametric mode.
26. Be able to identify relations and their inverses from their graphs, given information about either the function or the inverse.
27. Be able to determine general solutions to inverse trig functions.
28. Be able to explain how to create the graph of a circle in either funcion graphing mode or parametric graphing mode.
29. Be able to use calculators to determine values for all six trig functions.
30. Be able to use calculators to determine values for all six inverse trig functions.
Link to MA106 Trigonometry Home Page
Link to Ellerbruch Web Site Home Page
Link to Northern Michigan University
L. W. Ellerbruch: LELLERBR@nmu.edu.