25. a. sin 11m b. sin
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
the ones w the pink dot, make sure to show work

Transcribed Image Text:equal arcs, corresponding to t-values of
43. The number of hours of daylight, H, on day 1 of any given year
(on January 1,1 = 1) in Fairbanks, Alaska, can be modeled by
the function
5m 37 77
and 27.
4 2 4
4 2 4
27
H() = 12 + 8.3 sin
365 (
- )
a. Use the (x, y) coordinates in the figure to find the value of
the trigonometric function.
b. Use periodic properties and your answer from part (a) to
find the value of the same trigonometric function at the
a. March 21, the 80th day of the year, is the spring equinox.
Find the number of hours of daylight in Fairbanks on this
day.
b. June 21, the 172nd day of the year, is the summer solstice,
the day with the maximum number of hours of daylight.
To the nearest tenth of an hour, find the number of hours
of daylight in Fairbanks on this day.
c. December 21, the 355th day of the year, is the winter
solstice, the day with the minimum number of hours of
daylight. Find, to the nearest tenth of an hour, the number
of hours of daylight in Fairbanks on this day.
indicated real number.
(0, 1)
(-1,0)
|(1,0)
(- -
44. The number of hours of daylight, H, on day t of any given
year (on January 1, 1 = 1) in San Diego, California, can be
modeled by the function
(0, -1)
H() = 12 + 2.4 sin
365
(08 – 1)3
a. March 21, the 80th day of the year, is the spring equinox.
Find the number of hours of daylight in San Diego on this
day.
b. June 21, the 172nd day of the year, is the summer solstice,
the day with the maximum number of hours of daylight.
Find, to the nearest tenth of an hour, the number of hours
25. a. sin
26. a. cos
4
11
b. sin
4
117
b. cos
27. a. cos
28. a. sin
of daylight in San Diego on this day.
c. December 21, the 355th day of the year, is the winter
solstice, the day with the minimum number of hours of
daylight. To the nearest tenth of an hour, find the number
of hours of daylight in San Diego on this day.
b. cos
97
b. sin
2
29. a. tan 7
30. a. cot
b. tan 177
157
b. cot -
45. People who believe in biorhythms claim that there are three
cycles that rule our behavior-the physical, emotional, and
mental. Each is a sine function of a certain period. The
function for our emotional fluctuations is
31. a. sin
32. a. cos
477
b. sin
47
b. cos
4
E = sin t,
14
where t is measured in days starting at birth. Emotional
fluctuations, E, are measured from -1 to 1, inclusive, with
1 representing peak emotional well-being. -1 representing
the low for emotional well-being, and0 representing feeling
neither emotionally high nor low.
a. Find E corresponding to t = 7, 14,21,28, and 35. Describe
what you observe.
b. What is the period of the emotional cycle?
Practice Plus
In Exercises 33-42, let
sin i = a, cos t = b, and tan i = c.
Write each expression in terms of a, b, and c.
33. sin(-1) – sin t
34. tan(-r) – tan t
36. 3 cos(-1) – cos t
35. 4 cos(-1) – cos I
37. sin(t + 27) – cos(t + 47) + tan(t + 7)
46. The height of the water, H, in feet, at a boat dock t hours after
6 A.M. is given by
38. sin(t + 27) + cos(t + 47) – tan(t + #)
H = 10 + 4 sin t.
39. sin(-t – 27) – cos(-1 – 47) – tan(-t – 7)
40. sin(-1 - 27) + cos(-1 - 47) – tan(-t - 7)
41. cos t + cos(t + 10007) - tan t -
a. Find the height of the water at the dock at 6 A.M., 9 A.M.,
noon, 6 P.M., midnight, and 3 A.M.
b. When is low tide and when is high tide?
c. What is the period of this function and what does this
mean about the tides?
tan(t + 9997) – sin t +
4 sin(t – 10007)
42. -cos t + 7 cos(t + 10007) + tan t + tan(t + 9997) +
sin t + sin(t - 10007)
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