# Sine and Cosine in Real Life

#### zuhriri

Joined Jan 1, 2021
4
Hello, first of all, I'm sorry if this is not the place for this thread.

I want to ask, whether is my understanding about sine and cosine in real life is correct or not.

I came across this a question(about conventional DSB AM to be specified), where we have two signals

m(t) = 2sin(2000*pi*t) + 5sin(5000*pi*t) & c(t) = 100sin(2*pi*fc*t)

...and I need to determine the conventional DSB.

So, based on my understanding about sine and cosine in real life, they're quite similar because both are periodic signals and have the same shape(for example: sin(x) and cos(x)). The only difference is the phase of sine and cosine signals, which is 90deg out of phase to each other.

Hence, I believe it is valid to change the question to

m(t) = 2cos(2000*pi*t) + 5cos(5000*pi*t) & c(t) = 100cos(2*pi*fc*t)

...and still get the correct answer.

Is my understanding correct and if it is correct, is it really applicable in industries?

Thank you in advanced!

P.S. Sorry if my English is bad and if the question is too "beginner"

#### crutschow

Joined Mar 14, 2008
30,460
Is my understanding correct and if it is correct, is it really applicable in industries?
That would be correct, but it has no effect on the actual generation of the modulated signal, so would have no effect in "industries".

#### Wendy

Joined Mar 24, 2008
22,990
I have seen measurement system (on a IC pattern generator) where two signals generated by glass plates with fine chrome lines on two plates were used to optically generate a sine/cosine signal allowing for a x4 increase in measurement resolution. Not sur if this applies to your question but it is a real world application.

#### BobaMosfet

Joined Jul 1, 2009
2,009
Hello, first of all, I'm sorry if this is not the place for this thread.

I want to ask, whether is my understanding about sine and cosine in real life is correct or not.

I came across this a question(about conventional DSB AM to be specified), where we have two signals

m(t) = 2sin(2000*pi*t) + 5sin(5000*pi*t) & c(t) = 100sin(2*pi*fc*t)

...and I need to determine the conventional DSB.

So, based on my understanding about sine and cosine in real life, they're quite similar because both are periodic signals and have the same shape(for example: sin(x) and cos(x)). The only difference is the phase of sine and cosine signals, which is 90deg out of phase to each other.

Hence, I believe it is valid to change the question to

m(t) = 2cos(2000*pi*t) + 5cos(5000*pi*t) & c(t) = 100cos(2*pi*fc*t)

...and still get the correct answer.

Is my understanding correct and if it is correct, is it really applicable in industries?

Thank you in advanced!

P.S. Sorry if my English is bad and if the question is too "beginner"
Sine and Cosine are use to describe arcs in two planes- vertical and horizontal. That is why they are used together to represent a circle. However, in terms of how they are used in real-life, they are usually a means to describe an analog position of a point in space, in time. As time changes, the position changes, following one or the other, or both according to dimension.

The ability to interchange one for the other doesn't mean they are the same- because _you_ must understand they represent axis 90 degrees out of phase with one another. And unless you know which you are using- sine, or cosine, you don't know which axis is being worked with.

• justtrying

Joined Jul 18, 2013
25,654
I have seen measurement system (on a IC pattern generator) where two signals generated by glass plates with fine chrome lines on two plates were used to optically generate a sine/cosine signal allowing for a x4 increase in measurement resolution. Not sur if this applies to your question but it is a real world application.
Sounds like you are referencing quadrature encoders?
Typically the lines are photo etched into glass, The sine/cosine (quadrature) signal does not create the x4 signal, this is done by squaring up the two quadrature signals and using all 4 edges of the two pulses.
Once over a certain minimum resolution is reached, then a Moiré filter is used in order to magnify the 'shutter'.

#### Wendy

Joined Mar 24, 2008
22,990
Yep, didn't know what they were called I just had to align them, finicky.

Joined Jul 18, 2013
25,654
Yep, didn't know what they were called I just had to align them, finicky.
Many are under the impression that the term Quadrature is from method of using the X4 method of increasing the basic count.
When in fact it comes from the two 90° separated 'quadrature' wave forms.

#### Wendy

Joined Mar 24, 2008
22,990
I was refering to the end result. I was a tech not an engineer. I was given a PG3000 to repair after the 5V PS failed and blew every TTL device in the machine, and their were a lot of chips zapped. Got it working again, Had to replace a PROM chip that had a table for numerical values of a circle to the stepping motors. This gadget ran on a PDP Computer with 1KB of Bead ferrite memory. This being the late 90's.

Last edited:

Joined Jul 18, 2013
25,654
. This being the late 90's.
I hear you! The first linear scales (80's) I worked on had a incandescent lamp for light source and every time the lamp was replaced, the 90 °quadrature signal had to be realigned with a 'scope using Lissajous figures.

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#### Wendy

Joined Mar 24, 2008
22,990

Joined Jul 18, 2013
25,654
Yep. that was the one.
Oddly enough, the ones I referenced also interfaced to a PDP-8 12bit computer, running a CNC mill.

#### Wendy

Joined Mar 24, 2008
22,990
They replaced the computer with a 386 machine running an emulator some bright entrupenear cobbled up. They were glad to be rid of the bootup paper tape reader and magnetic reel. So was I.

• Deleted member 115935

#### Motanache

Joined Mar 2, 2015
540
m(t) = 2sin(2000*pi*t) + 5sin(5000*pi*t) & c(t) = 100sin(2*pi*fc*t)
.................
Hence, I believe it is valid to change the question to

m(t) = 2cos(2000*pi*t) + 5cos(5000*pi*t) & c(t) = 100cos(2*pi*fc*t)

...and still get the correct answer.
Is not correct.
Is... Between sine and cosine there is a "phase shift" of Pi / 2.
If m (t) and c (t) had not been present it would have been correct.

• xox

#### MrChips

Joined Oct 2, 2009
26,802
Sine and cosine are used in stepper motors to go from 1.8° per step to 100 microsteps.

#### nsaspook

Joined Aug 27, 2009
10,129

#### MrAl

Joined Jun 17, 2014
9,355
Hello, first of all, I'm sorry if this is not the place for this thread.

I want to ask, whether is my understanding about sine and cosine in real life is correct or not.

I came across this a question(about conventional DSB AM to be specified), where we have two signals

m(t) = 2sin(2000*pi*t) + 5sin(5000*pi*t) & c(t) = 100sin(2*pi*fc*t)

...and I need to determine the conventional DSB.

So, based on my understanding about sine and cosine in real life, they're quite similar because both are periodic signals and have the same shape(for example: sin(x) and cos(x)). The only difference is the phase of sine and cosine signals, which is 90deg out of phase to each other.

Hence, I believe it is valid to change the question to

m(t) = 2cos(2000*pi*t) + 5cos(5000*pi*t) & c(t) = 100cos(2*pi*fc*t)

...and still get the correct answer.

Is my understanding correct and if it is correct, is it really applicable in industries?

Thank you in advanced!

P.S. Sorry if my English is bad and if the question is too "beginner"
The steady state solution after a reasonably long time would often be considered the same because very often we dont really have a zero degree phase reference. There are applications that would go very wrong however if the zero degree phase was wrong. Time domain solutions of networks often have sin and/or cos terms and if you swap the sin and cos you will get the wrong start up solution even though the steady state will look the same except for phase. Some problems will not work at all like that though not even after a long time.

Many questions like this and their answers are application dependent. If you adopt a shortcut rule of thumb for something you have to remember that a day might come when it does not work for some new problem.