# Complex Question (1 Viewer)

#### tywebb

##### dangerman
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

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#### hmim

##### Member
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

##### dangerman
3 ways.

1. Check with calculator

and

2. Use sum to product

and

3. Use symmetry

and

• hmim and synthesisFR

#### synthesisFR

##### Well-Known Member
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

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• hmim

#### hmim

##### Member
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

##### Member
3 ways.

1. Check with calculator

and

2. Use sum to product

and

3. Use symmetry

and

Thanks! Method 3 looks useful

#### Drongoski

##### Well-Known Member
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:

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• hmim