5-3 Solving Trigonometric Equations Worksheet With Answers Page 25
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28in years.
a. What is the amplitude of the function? What does
it represent?
5-3 Solving Trigonometric Equations
b. What is the period of the function? What does it
represent?
c. Graph the function.
68.
csc
, cos =
, csc
< 0
SOLUTION:
SOLUTION:
a. The amplitude of the function is |a| = |20,000| or
20,000. The amplitude represents the amount that the
Use the Pythagorean Identity that involves cos θ.
population varies above and below the initial
population of 30,000.
b. The period of the function is
The population will return to its original value every
20 years.
Create a table listing the coordinates of the x-
Since one of the conditions is that csc θ < 0,
intercepts and extrema for f (x) = sin x for one
period, 2 , on the interval [0, 2 ]. Then use the
.
amplitude of g(x) to find corresponding points on its
graph.
69.
sec
; tan
= –1, sin
< 0
Functions
Max
Min
Max
SOLUTION:
(0, 50)
(10, 10)
(20, 50)
Use the Pythagorean Identity that involves tan
.
Sketch the curve through the indicated points for the
function. Then repeat the pattern to complete a
second period.
Since tan
is negative and sin θ is negative, cos
and sec θ must be positive. Therefore,
.
70.
POPULATION The population of a certain species
of deer can be modeled by p = 30,000 + 20,000
cos
, where p is the population and t is the time
in years.
a. What is the amplitude of the function? What does
it represent?
2
Given f (x) = 2x
– 5x + 3 and g(x) = 6x + 4, find
b. What is the period of the function? What does it
each of the following.
represent?
71.
(f – g)(x)
c. Graph the function.
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Page 25
SOLUTION:
SOLUTION:
a. The amplitude of the function is |a| = |20,000| or
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