Math 1119

Chapter 5 Review

Leslie

1. Find P(x, y) on the unit circle, given that the y-coordinate of P is and P is in quadrant III.
2. On the unit circle, determine which quadrant contains the terminal point of the arc whose length is -2.5.
3. Find the terminal point P(x, y) on the unit circle determined by the value t = .
4. Find the terminal point P(x, y) on the unit circle determined by the value t = .
5. Suppose the terminal point determined by t is the point . Find the terminal point determined by each of the following.
1. 
2. –t
3. 
4. 
6. Find the reference number for t =.
7. Find the reference number and the terminal point P(x, y) determined by t =.
8. Find the exact values of the following:
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. Find the terminal point when t is )
10. If the terminal point determined by t is , find the values of the six trigonometric functions.
11. If the terminal point determined by t is, find the values of the six trigonometric functions.
12. Find the approximate values to two decimal points for cos(6.1), csc(5.3), and tan(4.7).
13. Find the values of the six trigonometric functions of t given that sect = -3 and tan t > 0.
14. Determine algebraically whether the function is odd, even or neither.
15. Fill in the following chart:

t	0				1
Sin t
Cos t

16. Graph the following functions. State the amplitude, period and phase shift where applicable. Also determine the domain and range of each function.
1. f(x) = 2 – sin 4x
2. g(x) = |2cos x|
3. h(x) = ½ + ½ cos x
4. j(x) = tan 2x
5. k(x) = ¼ csc (x + 2)
6. 
7. 

17. The following table shows the average highs for each month in St. Paul, Minnesota from the years 1971-2000. Use the data and your calculator to find a sinusoidal curve which fits the data:

	Jan	Feb	Mar	Apr	May	June	July	Aug	Sept	Oct	Nov	Dec
High Temp	22.8	29.7	41.7	58.2	71.2	79.1	83.2	80.8	71.8	59.4	48.5	26.7

18. Suppose that the length of time between consecutive high tides is approximately 12.5 hours. According to the National Oceanic and Atmospheric Administration, on Saturday, June 28 1997, in Juneau, Alaska, high tide occurred at 8:11 AM (8.1833 hours) and low tide occurred at 2:14 PM (14.2333 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 13.2 feet and the height of the water at low tide was 2.2 feet.
1. Approximately when will the next high tide occur?
2. Find a sinusoidal function of the form that fits the data.
3. Use the function found in part b to predict the height of the water at the next high tide.

19. Given the graph below, determine its equation f(x) = asin(b(x-c)) + d