Chapter Test
Chapter
Chapter 6
Section
Chapter Test
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Solutions 8 Videos

Which trigonometric function has an asymptote at x = \frac{5\pi}{2} ?

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Q1

Which expression does not have the same value as all the other expressions?

\displaystyle \sin \frac{3\pi}{2}, \cos \pi, \tan \frac{7\pi}{4}, \csc \frac{3\pi}{2}, \sec 2\pi, \cot \frac{3\pi}{4}

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Q2

The function y= \cos x is reflected in the x-axis, vertically stretched by a factor of 12, horizontally compressed by a factor of 3, horizontally translated 6 units to the left, and vertically translated 100 units up. Determine the value of the new function, to the nearest tenth, when x = \frac{5\pi}{4}.

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Q3

The daily high temperature of a city, in degrees Celsius, as a function of the number of days into the year, can be described by the function \displaystyle T(d) = -20\cos(\frac{2\pi}{365}(d -10)) + 25 . What is the average rate of change, in degrees Celsius per day, of the daily high temperature fo the city from February 21 to May 8?

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Q4

Arrange the following angles in order, from smallest to largest:

\displaystyle \frac{5\pi}{8}, 113^o, \frac{2\pi}{3}, 110^o, \frac{3\pi}{5}

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Q5

Write an equivalent sine function for \displaystyle y = \cos(x + \frac{\pi}{8}) .

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Q6

The point (5, y) lies on the terminal arm of an angle in standard position. If the angle measures 4.8775 radians, what is the value of y to the nearest unit?

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Q7

The temperature, T, in degrees Celsius, of the surface water in a swimming pool varies according to the following graph, where t is the number of hours since sunrise at 6 a.m.

a) Find a possible equation for the temperature of the surface water as a function of time.

b) Calculate the average rate of change in water temperature from sunrise to noon.

c) Estimate the instantaneous rate of change in water temperature at 6 p.m.

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Q8