91Ó°ÊÓ

Solve the given problems. The horizontal displacement \(d\) (in \(\mathrm{m}\) ) of the bob on a large pendulum is \(d=5 \sin t,\) where \(t\) is the time (in s). Graph two cycles of this function.

Use a calculator to display the Lissijous figures defined by the given parametric equations. $$x=2 \sin \pi t, y=3 \sin 3 \pi t$$

Graph the given functions. In Exercises 27 and 28 use the equations for negative angles in Section 8.2 to first rewrite the function with a positive angle, and then graph the resulting function. $$y=0.4|\sin 6 x|$$

Solve the given problems. Display the graphs of \(y=2 \sin 3 x\) and \(y=2 \sin (-3 x)\) on a calculator. What conclusion do you draw from the graphs?

Solve the given problems. The displacement \(y\) (in \(\mathrm{cm}\) ) of the end of a robot arm for welding is \(y=4.75 \cos t,\) where \(t\) is the time (in s). Display this curve on a calculator.

Use a calculator to display the Lissijous figures defined by the given parametric equations. $$x=\frac{3 t}{1+t^{3}}, y=\frac{3 t^{2}}{1+t^{3}}$$

Solve the given problems. Display the graphs of \(y=2 \cos 3 x\) and \(y=\cos (-3 x)\) on a calculator. What conclusion do you draw from the graphs?

Solve the given problems. By noting the periods of \(\sin 2 x\) and \(\sin 3 x,\) find the period of the function \(y=\sin 2 x+\sin 3 x\) by finding the least common multiple of the individual periods.

Solve the given problems. By noting the period of \(\cos \frac{1}{2} x\) and \(\cos \frac{1}{3} x,\) find the period of the function \(y=\cos \frac{1}{2} x+\cos \frac{1}{3} x\) by finding the least common multiple of the individual periods.

Use a calculator to display the Lissijous figures defined by the given parametric equations. $$x=2 \sin 2 t, y=\frac{2 \sin ^{3} 2 t}{\cos t}$$