Complex Question (1 Viewer)

[hmim]

for the question 32x^5 - 40x^3 +10x -1 = 0 (leave your answer in terms of sin theta:

In this solution, i'm confused why 49pi/30 and 53pi/30 aren't included as part of the values of x?

Could someone please explain

 

[tywebb]

There have to be only 5 distinct answers. sin(49pi/30) and sin(53pi/30) are included because

and



So it matters not if you list them as

or



but to keep them distinct for example you can't have and in the list because they are the same.

I just think they chose the smallest values of to use in the list.

A simpler example would be to list instead of

 

[hmim]

There have to be only 5 distinct answers. sin(49pi/30) and sin(53pi/30) are included because

and



So it matters not if you list them as

or



but to keep them distinct for example you can't have and in the list because they are the same.

I just think they chose the smallest values of to use in the list.

A simpler example would be to list instead of

Hmm, how did you find that

and

??

I'm a bit confused. I know its equal but how did you get it?
Any help would be appreciated, thanks

 

[tywebb]

3 ways.

1. Check with calculator

and

2. Use sum to product

and



3. Use symmetry

and

 

[synthesisFR]

Hmm, how did you find that

and

??

I'm a bit confused. I know its equal but how did you get it?
Any help would be appreciated, thanks

for these questions i was taught to always draw the unit circle
so for example this:

and
sin 45pi/30 would be the negative y axis bc its 3pi/2, with 49pi/30 and 41pi/30 equally spaced on each side. Sin is negative in 3rd and quadrant, and both these angles represent the same length bc its equally spaced from sin45pi/30, so they would give the same values, so u cancel one out.
Also for exams i was told to always use the smaller angle if it repeats so u would take 41pi/30. lmk if u need a diagram

 

[hmim]

for these questions i was taught to always draw the unit circle
so for example this:

and
sin 45pi/30 would be the negative y axis bc its 3pi/2, with 49pi/30 and 41pi/30 equally spaced on each side. Sin is negative in 3rd and quadrant, and both these angles represent the same length bc its equally spaced from sin45pi/30, so they would give the same values, so u cancel one out.
Also for exams i was told to always use the smaller angle if it repeats so u would take 41pi/30. lmk if u need a diagram

Ohh thanks, that makes sense. It would be great if you could provide the diagram though!

 

[hmim]

3 ways.

1. Check with calculator

and

2. Use sum to product

and



3. Use symmetry

and

Thanks! Method 3 looks useful

 

[Drongoski]

Another way to look at it:


have the same related angles (11pi/30) and they are both negative, being in the 3rd & 4th quadrants resp. Similarly: