Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![Example 5
(page 751)
Use the graph of the appropriate reciprocal trigonometric function to find
each value. Round to four decimal places.
33. sec 30°
34. sec 80°
35. sec 110°
36. csc 30°
37. csc 70°
38. csc 130°
39. cot 30°
40. cot 60°
Example 6
(page 752)
41. Indirect Measurement A communications tower has wires anchoring it to the
ground. Each wire is attached to the tower at a height 20 ft above the ground.
The length y of the wire is modeled with the function y = 20 csc 0, where 0 is
the measure of the angle formed by the wire and the ground.
a. Graph the function.
b. Find the length of wire needed to form an angle of 45°.
c. Find the length of wire needed to form an angle of 60°.
d. Find the length of wire needed to form an angle of 75°.
ply Your Skills
Evaluate each expression. Write your answer in exact form. If appropriate, also
state it as a decimal rounded to the nearest hundredth. If the expression is
undefined, write undefined.
42. cot (-45°)
43. sec (-30°)
44. csc (-90°)
45. sec (-180°)
Graph each function in the interval from 0 to 2r.
46. y = csc 0-5
47. y = sec 0
48. y = -sec TO
49. y = cot
g
Match each function with its graph.
50. y =
51. y = cos X
%3D
COS
sin x
52. y =
53. y =
tan x
sin x
В.
А.
UN
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