MTH 164 INTRODUCTION TO TRIGONOMETRY

1. Define radians as a measure of angle rotation.

2. Draw an approximate diagram in standard position on coordinate axes of an angle given in radians.

3. State whether or not an angle drawn on coordinate axes is in standard position.

4. Find positive and negative coterminal angles for an angle in standard position.

5. State the six trigonometric ratios (in terms of x, y, and r) for an angle in standard position whose terminal side passes through a point (x,y) on a circle of radius r.

6. Using points on a unit circle, find the exact values of the six trigonometric ratios of quadrantal angles (0, p /2, p , 3p /2, 2p ) and special angles (p /4, p /6, p /3).

7. Determine whether a trigonometric ratio of an angle in standard position is positive or negative.

8. Find the reference angle for an angle in standard position.

9. Find the exact value of a trigonometric ratio of an angle whose reference angle is a special angle.

10. Use a calculator to find the approximate value of a trigonometric ratio of an angle given in radians.

11. Draw the graph and state the domain, range, x-intercepts, and y-intercept of
y = sin x and y = cos x.

12. Use a calculator to draw graphs of the form y = a sin x and y = a cos x. Determine amplitude and its effect on the graph.

13. Draw the graph and state the domain, range, and asymptotes of y = tan x and y = cot x.

14. Use the graphs of y = sin x and y = cos x to draw the graphs of y = csc x and y = sec x. State the domain, range, and asymptotes.

15. Use reciprocal and quotient identities, and the Pythagorean identity sin2x+cos2x = 1 to establish new trigonometric identities.

16. Solve first degree trigonometric equations for exact values of the variable as well as for approximate values.

17. Convert the measure of an angle given in radians to decimal degrees, and convert the measure of an angle given in decimal degrees to radians.

18. Convert the measure of an angle given in decimal degrees to degrees, minutes, seconds (DMS) form, and convert the measure of an angle given in DMS form to decimal degrees.

19. Use a calculator to find the approximate value of a trigonometric ratio of an angle given in decimal degrees or DMS form.

20. Solve a right triangle when given one acute angle and one side, or two sides.

21. Use the Law of Sines to solve an oblique triangle when given two angles and one side, or two sides and an angle opposite one of those sides, excluding the ambiguous case.

22. Use the Law of Cosines to solve an oblique triangle when given two sides and the included angle, or three sides.

23. Solve applied problems involving right or oblique triangles.

(revised 9/17/01)