5-3 Solving Trigonometric Equations Worksheet With Answers Page 13
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28cos
+ 66.95. Because x = 1 represents
January 15, x = 1.5 represents January 31. Use the
On the interval
, the only solution is when x =
5-3 Solving Trigonometric Equations
TRACE feature to determine the temperature when
1.34.
x = 1.5.
39.
x log x + 5x cos x = –2
SOLUTION:
Therefore, the temperature on January 31 is about
61.3º.
b. Graph y = 70. Then use the intersect feature
under the CALC menu to determine the interval on
which 8.05 cos
+ 66.95 > 70.
On the interval
, the solutions are when x =
1.84 and when x = 4.49.
40.
METEOROLOGY The average daily temperature
in degrees Fahrenheit for a city can be modeled by t
= 8.05 cos
+ 66.95, where x is a function of
time, x = 1 represents January 15, x = 2 represents
February 15, and so on.
a. Use a graphing calculator to estimate the
temperature on January 31.
b. Approximate the number of months that the
So, 8.05 cos
+ 66.95 > 70 on the interval
average daily temperature is greater than 70
throughout the entire month.
3.74 < x < 8.26. Because x = 3.74 corresponds to
c. Estimate the highest temperature of the year and
about the middle of April, the temperature does not
the month in which it occurs.
exceed 70º for the entire month until May.
Therefore, the average daily temperature is greater
SOLUTION:
than 70º for the entire month during the months of
a. Use a graphing calculator to graph t = 8.05
May, June, and July. Therefore, the average
temperature was higher than 70º for three months.
cos
+ 66.95. Because x = 1 represents
c. Use the maximum feature under the CALC
January 15, x = 1.5 represents January 31. Use the
menu to find the maximum value of the function on
TRACE feature to determine the temperature when
[0, 12].
x = 1.5.
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Page 13
The maximum value is 75 when x ≈ 6. Therefore,
Therefore, the temperature on January 31 is about
the maximum average monthly temperature is 75º
61.3º.
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