3u yr 11 questions, thanks (1 Viewer)

[currysauce]

1) Solve equation

cos2A = cosA where 0 < A < 360


^ i can't do these expansions properly, so stuck at first section

If sinα = 3/4 where 0 < α < π/2 and sinβ = 2/3 where π/2 < β < π

( thingy that loks like n is pi)

find the exact value of

tan 2(alpha)

 

[Xayma]

cos 2&alpha;=cos &alpha;
2cos² &alpha;-1=cos &alpha;
2cos² &alpha;-cos &alpha;-1=0
(2cos &alpha;+1)(cos &alpha;-1)=0
Therefore it occurs when:

cos &alpha;=1
&alpha;=0&deg; or &alpha;=360&deg; (Although going by the initial definition of 0 < &alpha; <360 these are not solutions)

OR 2cos &alpha;=-1
cos &alpha;=-1/2
&alpha;=120&deg; &alpha;=240&deg;

___________________________________________________
Right angled triangle: Other side= &radic;7

tan 2&alpha;=2tan&alpha;/(1-tan² &alpha;.)

So just sub in tan &alpha;=3/&radic;7

 

[currysauce]

2nd

isn't is tan a = 3/ root 7 seeing as 16-9 = 7?

so i sub 3/root7 into the tan expansion and got

-42/2root7

doesn't look right

 

[~*HSC 4 life*~]

isn't is tan a = 3/ root 7 seeing as 16-9 = 7?

so i sub 3/root7 into the tan expansion and got

-42/2root7

doesn't look right

i got the same thing too

 

[mojako]

isn't is tan a = 3/ root 7 seeing as 16-9 = 7?

so i sub 3/root7 into the tan expansion and got

-42/2root7

doesn't look right

firstly, there's nothing strange with getting -42/2root7 for a value of tan(x)....

but anyway, I got -3*sqrt(7)

but now im confused.. what is beta for??

 

[Supra]

yah i dont c how beta is useful...and i got -42/2√7 btw

 

[mojako]

yah i dont c how beta is useful...and i got -42/2√7 btw

after some confusion, I discovered that -42/2sqrt(7) is the same as -3sqrt(7)

 

[Xayma]

firstly, there's nothing strange with getting -42/2root7 for a value of tan(x)....

but anyway, I got -3*sqrt(7)

but now im confused.. what is beta for??

I'm guessing that it was used for a seperate part that they could complete.

 

[AreYouAlright?]

Yeah.. -3*root7

Haha yeah beta seems pretty useless in that question but isn't it true that -3*root7 would be the more correct answer as you should never have an irrational number on the denominator?

 

[mojako]

Haha yeah beta seems pretty useless in that question but isn't it true that -3*root7 would be the more correct answer as you should never have an irrational number on the denominator?

in the extension courses they usually don't care about irrational denominator
correct me if im wrong.

 

[AreYouAlright?]

No, you're probably right

I'm probably thinking about the 2u course i suppose they would expect u just to know that in the extension courses.

 

[Slidey]

My teacher constantly leaves it with an irrational denominator, which irks me, but... yea, it doesn't matter terribly much.