Sin(5x) = 1 (I just can't seem to figure it out)

[Pipkin]

Sin(5x)=1

I just can't seem to figure it out. Can anyone help?

 

[arthur ohlsten]

Re: Sin(5x)=1

sin[5x]=1
5x=pi/2, or pi/2+2pi, or pi/2 +4pi , etc.
x=pi/10 or x= pi/10+2pi/5 or x= pi/10 + 4pi/5 etc.

sin[5x]=1
5x=90, or 450, or 810, or n[360] +90
x=18 degrees or [18 + n[72] ] degrees n=0,1,2,...

Arthur

 

[mmm4444bot]

I hope you understand radian measure because that's what I'm using, in the following statements.

Do you know the measure of the angle between 0 and 2? that has a sine value of 1?

In other words, what is the measure of angle Theta below?

sin(?) = 1

If you cannot figure this out, then you are not ready to do your exercise.

Here's a similar example.

cos(4x) = 1/2

We know that cos(?/3) = 1/2, and we also know that cos(5?/3) = 1/2.

In other words, the angles ?/3 and 5?/3 are the two angles between 0 and 2? that have a cosine value of 1/2.

Now, I add integer multiples of 2? (i.e., the period of cosine) to both of these angles, in order to express ALL angles that have a cosine value of 1/2:

?/3 + 2?k, where k is an integer

5?/3 + 2?k, where k is an integer

Finally, to find all of the values of x such that cos(4x) = 1/2, I set the expressions above equal to 4x and solve for x.

4x = ?/3 + 2?k

4x = 5?/3 + 2?k

Divide both sides by 4.

x = ?/12 + (?/2)k, where k is an integer

x = 5?/12 + (?/2)k, where k is an integer

Your exercise may be solved using the same strategy.

If I wrote anything that you do not understand, then please ask specific questions. If you need more help, then show your work, so that somebody might determine where to continue helping you.

 

[mmm4444bot]

Or, you could simply copy Arthur's work, and turn it in as your own.

(If you do, then I hope your teacher ignores negative angles, just like Arthur does. :wink: )

 

[arthur ohlsten]

there was no restriction on n [x= pi/10 + npi/5 n a integer -oo<n<00 to be complete]

I assumed (probably erroneously) the instructor would only be interested in the value of x when n=0

I also did not know if the student had to work in radians or degrees.

When the student sees how the problem was solved he should redo the work on his own
Arthur

 

[mmm4444bot]

… n=0,1,2,...

there [is] no restriction on n …

Arthur, are you sure that you do not understand the restriction that you placed on the values of n (above)? :?

The set {0, 1, 2, 3, …} is the set of Whole numbers (AKA the Non-Negative Integers only).

'

… n [an] integer -oo<n<00 … :?

Is this really how you teach your students to express the set of integers?

'

… the student … should redo the work …

In an ideal world, I would agree with this.

I thought you previously agreed not to do students' homework for them. I thought you previously agreed that you would provide similar examples, instead.

Perhaps, I'm confusing you with somebody else.