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Magazine Problem 3
\(3-16\) Graph the function. $$ f(x)=1+\cos x $$
Problem 3
\(3-10=\) Find the exact value of each expression, if it is defined. $$ \begin{array}{lll}{\text { (a) } \sin ^{-1} 1} & {\text { (b) } \sin ^{-1} \frac{\sqrt{3}}{2}} & {\text { (c) } \sin ^{-1} 2}\end{array} $$
Problem 3
The given function models the displacement of an object moving in simple harmonic motion. (a) Find the amplitude, period, and frequency of the motion. (b) Sketch a graph of the displacement of the object over one complete period. $$ y=2 \sin 3 t $$
Problem 3
\(3-8 \approx\) Show that the point is on the unit circle. $$ \left(\frac{4}{5},-\frac{3}{5}\right) $$
Problem 4
\(3-16\) Graph the function. $$ f(x)=3+\sin x $$
Problem 4
The given function models the displacement of an object moving in simple harmonic motion. (a) Find the amplitude, period, and frequency of the motion. (b) Sketch a graph of the displacement of the object over one complete period. $$ y=3 \cos \frac{1}{2} t $$
Problem 4
\(3-8 \approx\) Show that the point is on the unit circle. $$ \left(-\frac{5}{13}, \frac{12}{13}\right) $$
Problem 5
Find the exact value of the trigonometric function at the given real number. (a) \(\sin \frac{2 \pi}{3} \quad\) (b) \(\cos \frac{2 \pi}{3} \quad\) (c) \(\tan \frac{2 \pi}{3}\)
Problem 5
The given function models the displacement of an object moving in simple harmonic motion. (a) Find the amplitude, period, and frequency of the motion. (b) Sketch a graph of the displacement of the object over one complete period. $$ y=-\cos 0.3 t $$
Problem 5
\(3-10=\) Find the exact value of each expression, if it is defined. $$ \begin{array}{llll}{\text { (a) } \cos ^{-1}(-1)} & {\text { (b) } \cos ^{-1} \frac{1}{2}} & {\text { (c) } \cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)}\end{array} $$
