SAT II math

Discus: SAT/ACT Tests and Test Preparation: June 2004 Archive: SAT II math
 By Satchamp (Satchamp) on Thursday, June 03, 2004 - 09:49 pm: Edit

1. Which of the following values is defined?
(A) arcsin 2
(B) tan 90
(C) sec 90
(D) arctan 0
(E) cot 270

2. S and T are the centers of their respective circles. The two circles are mutually tangent at point U. If segment RS = d, what is the radius of the smaller circle in terms of d and ?
(A) d cos A
(B) d sin A
(C) d(cosA – sinA)
(D) d(sinA – cosA)
(E) d(sinA + cosA)

hey...the 1st one is D and the second one is C

cud u plz explain Why???

 By Baseballnbooks (Baseballnbooks) on Thursday, June 03, 2004 - 10:07 pm: Edit

1. (d)

I dont know 2

 By Qwert271 (Qwert271) on Thursday, June 03, 2004 - 10:12 pm: Edit

1. the tangent of 0 degrees equals 0, therefore there is an angle that when put into the tan formula, you will get 0. B, C, and E are infinite, and A is just plain impossible.

2. You may not have given us all the info that you have because you're introducing variables and letters that you never defined.

 By Satchamp (Satchamp) on Thursday, June 03, 2004 - 10:43 pm: Edit

oooh......there was a diagram..never mind that

but isnt cot270 =0 ??
SO THAT WOULD BE DEFINEd right?

 By Qwert271 (Qwert271) on Thursday, June 03, 2004 - 10:46 pm: Edit

I think you're right. I just skipped over it without reading. My bad. Maybe it's a typo, either way I wouldn't worry about it.

 By Satchamp (Satchamp) on Thursday, June 03, 2004 - 10:56 pm: Edit

also technically,
doesnt arctan0 have infinite values....
coz only Arctan0=0
while arctan0= 0, 180, 360 and so on.
its an example online at the sparknotes website.....i got the link
http://www.sparknotes.com/testprep/books/sat2/math2c/chapter9section12.rhtml

yeah.....check it out

 By R2005 (R2005) on Friday, June 04, 2004 - 01:03 am: Edit

Satchamp...

sparknotes says the answer is d.

BUT, cot=1/tan OR cos/sin

sin 1.5pi=1
cos 1.5pi=0
so, tan (sin/cos)1.5pi = impossible

BUT, cot (cos/sin)1.5pi= 0/1= 0=defined

but d, after plugging into my calculator, is defined as well.

BUT, when i type in 1/tan(1.5pi) in it, it's ERROR..

WTF?

help help help

 By Aim78 (Aim78) on Friday, June 04, 2004 - 01:09 am: Edit

Think of cot as 1/tan, not cos/sin. In order for it to be defined, it has to work with BOTH of those definitions.

270 degrees = 3pi/2
tan(3pi/2) = -1/0 = undefined
1/undefined = undefined

 By Madd87 (Madd87) on Friday, June 04, 2004 - 12:12 pm: Edit

arctan's domain is -infinity to infinity, so the answer is obviously D

 By Satchamp (Satchamp) on Friday, June 04, 2004 - 12:29 pm: Edit

but i always thought that cot270=0

what does being defined really mean??

 By Satchamp (Satchamp) on Friday, June 04, 2004 - 12:51 pm: Edit

hey now.......cot of an angle = opposite/adjactent
....now wudnt that be equal to 0 .....at cot270
this is soo weird....

 By Monoe (Monoe) on Friday, June 04, 2004 - 03:14 pm: Edit

Cotangent is adjacent over opposite, not opposite over adjacent. It is the inverse of tangent.

 By Joshjmgs (Joshjmgs) on Friday, June 04, 2004 - 03:17 pm: Edit

madd, sorry but thats not true, arctan is only defined in the first and fourth quadrants.

and
arcsin is defined in the first are fourth quadrants
arccos is defined in the first and SECOND quadrants

 By Joshjmgs (Joshjmgs) on Friday, June 04, 2004 - 03:19 pm: Edit

" Cotangent is adjacent over opposite, not opposite over adjacent. It is the inverse of tangent."

Cotangeant the reciprocal on tangeant, the inverse of tangeant is arctan!

I dont mean to be so onol (o=>a) about the wording, but its kind of important to know the difference for the IIc.

 By Satchamp (Satchamp) on Friday, June 04, 2004 - 04:14 pm: Edit

isnt arctan different from Capital Arctan...
4get it.doesnt matter.......
so technically cot0 as well as cot 90 are undefined???