auxiliary angles q (1 Viewer)

[indeed]

From 2022 hsc, im sure ppl in the past have prob asked this



The final answer they give is ...x- pi/3, but the Q wants x+...

Did they write this wrong or something or?

 

[mmmmmmmmaaaaaaa]

no, alpha is in quadrant 4

 

[indeed]

no, alpha is in quadrant 4

Then since it's in 4th quad and question wants a positive angle then shouldn't you just +2pi

 

[mmmmmmmmaaaaaaa]

Then since it's in 4th quad and question wants a positive angle then shouldn't you just +2pi

no because that would be in the 2nd quadrant

 

[indeed]

no because that would be in the 2nd quadrant

Adding 2pi is adding a full revolution, that would result in arriving at the 4th quad again

 

[SB257426]

From 2022 hsc, im sure ppl in the past have prob asked this
View attachment 40199
View attachment 40200

The final answer they give is ...x- pi/3, but the Q wants x+...

Did they write this wrong or something or?

I think it should be x+5pi/3 instead

 

[SB257426]

I think it should be x+5pi/3 instead

remember the '-pi/3' is "equivalent" to an angle in the fourth quadrant. So that equivalent angle would be 5pi/3.. I think

 

[mmmmmmmmaaaaaaa]

Adding 2pi is adding a full revolution, that would result in arriving at the 4th quad again

yes sorry I get that but what would the point be of adding 2pi

the question isn't asking for a positive

think of it link Rsin(x+(-alpha)) in this scenario

 

[indeed]

remember the '-pi/3' is "equivalent" to an angle in the fourth quadrant. So that equivalent angle would be 5pi/3.. I think

Yh agreed

 

[indeed]

yes sorry I get that but what would the point be of adding 2pi

the question isn't asking for a positive

think of it link Rsin(x+(-alpha)) in this scenario

But if they wanted a negative, they have always explicitly stated a negative sign (I've seen like 20+ auxiliary Q's that have followed this pattern but the HSC is the only one to break this pattern)

 

[synthesisFR]

no they havent broken any rule or anything... its just that they asked for a different auxillary expression
usually u would be given Rsin(x-alpha) for those questions like the one above so that the negative just cancels each other out (because alpha would be positive then), but its really just the same thing the final result would be the same.

But if they wanted a negative, they have always explicitly stated a negative sign (I've seen like 20+ auxiliary Q's that have followed this pattern but the HSC is the only one to break this pattern)

it isn't related to wanting a negative angle ur thinking about it in the wrong way

 

[mmmmmmmmaaaaaaa]

But if they wanted a negative, they have always explicitly stated a negative sign (I've seen like 20+ auxiliary Q's that have followed this pattern but the HSC is the only one to break this pattern)

that would be a slightly different question though, so no

 

[indeed]

Oh ok thanks all

 

[SB257426]

But if they wanted a negative, they have always explicitly stated a negative sign (I've seen like 20+ auxiliary Q's that have followed this pattern but the HSC is the only one to break this pattern)

yeah the hsc tries some really quirky stuff somtimes... its gotten to the point where no one gives a fck anymore

 

[carrotsss]

But if they wanted a negative, they have always explicitly stated a negative sign (I've seen like 20+ auxiliary Q's that have followed this pattern but the HSC is the only one to break this pattern)

when they do this they typically state a restriction of 0<alpha<pi or 0<alpha<pi/2, in this case they haven't done that hence why a negative solution for alpha is present

 

[Trebla]

Both -pi/3 and 5pi/3 are correct. Just because the sample answer uses -pi/3 doesn't necessarily mean it's the only answer...

 

[indeed]

when they do this they typically state a restriction of 0<alpha<pi or 0<alpha<pi/2, in this case they haven't done that hence why a negative solution for alpha is present

Oh ok i see, yh i was wondering when to use the other form thanks

 

[indeed]

Both -pi/3 and 5pi/3 are correct. Just because the sample answer uses -pi/3 doesn't necessarily mean it's the only answer...

Oh ok, that's reassuring thanks