CIS problems

**wiseguy** · July 25th 2010, 11:45 AM

A small portion of the last chapter in my textbook is devoted to cis problems. It is very unclear about the cis trigometric function, providing no examples whatsoever.

Here are two problems from my textbook I attempted to work on:

"Write in a + bi form: $5 cis 300°$
Round the value of a to the hundredth.

Leave your answer in the form ___+___i"

and

"Multiply: $(6 cis 100°) (2 cis 70°)$
Leave your answer in the form ___cis___°"

If I could get an explanation on these two problems, I'll (hoprefully

) be able to work though the rest, and I'll have a good study session. I'm guaranteed at least one question on cis on my final.

At first I thought the folks who wrote the book made a typo for cos, given the "I" key on the keyboard is so close to the "O" key.

Many thanks in advance to quick help!

**tonio** · July 25th 2010, 01:15 PM

Originally Posted by wiseguy

A small portion of the last chapter in my textbook is devoted to cis problems. It is very unclear about the cis trigometric function, providing no examples whatsoever.

Here are two problems from my textbook I attempted to work on:

"Write in a + bi form: $5 cis 300°$
Round the value of a to the hundredth.

Leave your answer in the form ___+___i"

and

"Multiply: $(6 cis 100°) (2 cis 70°)$
Leave your answer in the form ___cis___°"

If I could get an explanation on these two problems, I'll (hoprefully

) be able to work though the rest, and I'll have a good study session. I'm guaranteed at least one question on cis on my final.

At first I thought the folks who wrote the book made a typo for cos, given the "I" key on the keyboard is so close to the "O" key.

Many thanks in advance to quick help!

You have to (1) understand that $cis(\theta):=\cos\theta+i\sin\theta$ , (2) you have to know pretty well your trigonometry and (3) you have to remember the definition $a+ib=\sqrt{a^2+b^2}\,cis\theta\,,\,\,\theta=\arcta n\frac{b}{a}\,,\,\,a,b\in\mathbb{R}\,,\,a\neq 0$ , and if $a=0\,,\,\,\theta=\frac{\pi}{2}+k\pi\,,\,\,k\in\mat hbb{Z}$ .

So let's do one, and you do the other one: $5\,cis(300^\circ)=5(\cos 300^\circ+i\sin 300^\circ)=5\left(\frac{1}{2}-\frac{\sqrt{3}}{2}i\right) = \frac{5}{2}-\frac{5\sqrt{3}}{2}i$

Tonio

**Archie Meade** · July 25th 2010, 01:16 PM

Originally Posted by wiseguy

A small portion of the last chapter in my textbook is devoted to cis problems. It is very unclear about the cis trigometric function, providing no examples whatsoever.

Here are two problems from my textbook I attempted to work on:

"Write in a + bi form: $5 cis 300°$
Round the value of a to the hundredth.

Leave your answer in the form ___+___i"

and

"Multiply: $(6 cis 100°) (2 cis 70°)$
Leave your answer in the form ___cis___°"

If I could get an explanation on these two problems, I'll (hoprefully

) be able to work though the rest, and I'll have a good study session. I'm guaranteed at least one question on cis on my final.

At first I thought the folks who wrote the book made a typo for cos, given the "I" key on the keyboard is so close to the "O" key.

Many thanks in advance to quick help!

Hi Wiseguy...

"cis" means "cos+isin"

so $cis(\theta)=cos\theta+isin(\theta)$

For a complex number a+bi..."a" is the real part and "bi" is the imaginary part.

$5cis300^o=5\left(cos300^o+isin300^o\right)$

hence ... $a=5cos300^o$ and $b=5sin300^o$

$6cis100^o2cis670^o=6\left(cos100^o+isin100^o\right )2\left(cos70^o+isin70^o\right)$

$=12\left(cos100^ocos70^o+icos100^osin70^o+icos70^o sin100^o-sin100^osin70^o\right)$

Now combine the real parts to get "a" and the imaginary parts to get "b"
after applying the appropriate trigonometric identities to them.

**wiseguy** · July 25th 2010, 02:57 PM

Originally Posted by tonio

You have to (1) understand that $cis(\theta):=\cos\theta+i\sin\theta$ , (2) you have to know pretty well your trigonometry and (3) you have to remember the definition $a+ib=\sqrt{a^2+b^2}\,cis\theta\,,\,\,\theta=\arcta n\frac{b}{a}\,,\,\,a,b\in\mathbb{R}\,,\,a\neq 0$ , and if $a=0\,,\,\,\theta=\frac{\pi}{2}+k\pi\,,\,\,k\in\mat hbb{Z}$ .

So let's do one, and you do the other one: $5\,cis(300^\circ)=5(\cos 300^\circ+i\sin 300^\circ)=5\left(\frac{1}{2}-\frac{\sqrt{3}}{2}i\right) = \frac{5}{2}-\frac{5\sqrt{3}}{2}i$

Tonio

Okay, I ended up with 12cis(-0.984807753)°
...this is the form they were asking for in the second question: "Leave your answer in the form ___cis___°"

**Archie Meade** · July 25th 2010, 04:05 PM

Originally Posted by wiseguy

Okay, I ended up with 12cis(-0.984807753)°
...this is the form they were asking for in the second question: "Leave your answer in the form ___cis___°"

From $12\left(cos100^ocos70^o-sin100^osin70^o+i[cos100^osin70^o+cos70^osin100^o]\right)$

you should use $cosAcosB-sinAsinB=cos(A+B)$

and $cosAsinB+cosBsinA=sin(A+B)$

where $A=100^0$ and $B=70^o$

to get $12cis(A+B)$

**wiseguy** · July 25th 2010, 08:13 PM

Which equals 12cis170°...?

**Archie Meade** · July 26th 2010, 01:21 AM

Originally Posted by wiseguy

Which equals 12cis170°...?

Yes,

you evaluated $cos170^o=-0.9848$

However $cis170^0=cos170^0+isin170^o$

Thread: CIS problems

LinkBack

Thread Tools

Display

CIS problems

Similar Math Help Forum Discussions

memory problems/concentration problems with age?

binomial problems/normal problems

binomial problems as normal problems

Problems with integration word problems

Help thease problems problems