91Ó°ÊÓ

Find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.

$y=4\sin \left(\mathrm{Ï€³\ae }+2\right)-5$

$si{n}^2\mathrm{θ}+co{s}^2\mathrm{θ}=$____.

if$\cos \left(\mathrm{θ}\right)=0.2$, then find the value of$\cos \left(\mathrm{θ}\right)+\cos \left(\mathrm{θ}+2\mathrm{π}\right)+\cos \left(\mathrm{θ}+4\mathrm{π}\right)$

If$f\left(x\right)=\cos \mathrm{θ}=0.3,$findrole="math" localid="1647539382705" $f(\mathrm{θ}+\mathrm{π})$

Alternating Current (ac) Generators The voltage V, in volts, produced by an ac generator at time t, in seconds, is

$V\left(t\right)=120\sin \left(120\mathrm{Ï€³Ù}\right)$

(a) What is the amplitude? What is the period?
(b) Graph V over two periods, beginning att=0.
(c) If a resistance of R=20 ohms is present, what is the currentI ?
[Hint: Use Ohm's Law, V=IR
(d) What is the amplitude and period of the current I.
(e) Graph Iover two periods, beginning att=0 .

Find the length $s$and area $A$. Round answers to three decimal places.

If$f\left(\mathrm{θ}\right)=\tan \mathrm{θ}=3$findrole="math" localid="1646573441822" $f\left(\mathrm{θ}+\mathrm{π}\right)$.

if$\tan \left(\mathrm{θ}\right)=3$then find$\tan \left(\mathrm{θ}\right)+\tan \left(\mathrm{θ}+\mathrm{π}\right)+\tan \left(\mathrm{θ}+2\mathrm{π}\right)$

Alternating Current (ac) Generators The voltage V produced by an ac generator is sinusoidal. As a function of time, the voltage V is

$V\left(t\right)=V_0\sin \left(2\mathrm{Ï€´Ú³Ù}\right)$

$P\left(t\right)=\frac{{\left[V\right(t\left)\right]}^2}{R}$

(c) Deduce that${\sin }^2\left(2\mathrm{Ï€´Ú³Ù}\right)=\frac{1}{2}[1-\cos (4\mathrm{Ï€´Ú³Ù}\left)\right]$

The minute hand of a clock is $6$inches long. How far does the tip of the minute hand move in $15$ minutes? How far does it move in $25$ minutes? Round answers to two decimal places.