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Subsection 2.4 Evaluating Trigonometric Functions Exercises
For each angle
\(\theta\) below, find
\(\sin \theta\text{,}\) \(\cos \theta\text{,}\) \(\tan \theta\text{,}\) \(\sec \theta\text{,}\) \(\csc \theta\) and
\(\cot \theta\text{.}\)
\(\displaystyle \theta=5 \pi\)
\(\displaystyle \theta=\frac{21\pi}{4}\)
\(\displaystyle \theta=-\frac{4\pi}{3}\)
\(\displaystyle \theta=-\frac{11\pi}{2}\)
Let
\(P(t)=4 \cos (2t)\text{.}\)
What is the average rate of change of
\(P(t)\) over the interval from
\(t=\frac{\pi}{4}\) to
\(t=\frac{2\pi}{3}\text{?}\)
Find all possible solutions to
\(P(t)=2\) on the interval
\(-2\pi \leq t < 2\pi\text{.}\)
Refer to
\(g(t)=2t^2 - 4t -1\text{.}\)
Graph the function
\(g(t)\) on the domain
\(-4 \leq t \leq 4\text{.}\) Be sure to label the vertex and any intercept(s).
Solve the inequality
\(g(t)<0\text{.}\)
Solve the inequality
\(g(t)<t^2-1\text{.}\)
What is the range of
\(g(t)\) on the domain of all real numbers?
\(\displaystyle 3^{3x}\cdot 3^{x-1}=15\)
\(\displaystyle \left(\frac{1}{2}\right)^{x}2^{3x+2}=11\)
Uranium-232 is a radioactive isotope with a half-life of 68.9 years.
Write an exponential equation to model the amount,
\(A(t)\text{,}\) remaining after
\(t\) years from an initial sample of 180 g.
How much of the sample will remain after 20 years?
When will the sample decay to 20 g?
Write an equation for the inverse function,
\(A^{-1}\text{?}\)
What are the units (grams, years?) of the input to
\(A^{-1}\text{?}\) What are the units of the output?
A shed is being constructed in the shape of an isosceles triangle as shown below. The city zoning laws say that sheds can be no taller than 10 feet tall at their tallest point. Will this shed be allowed under these laws?
Figure 2.4.26.
