powers/radical question PLEASE HELP!

[philapharm7]

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I'm taking the PCAT this Saturday so if you can answer this I would really really really appreciate it!!

I think the explanation for these 2 questions is the same, but just in case I'll give both examples:

(*=degrees, sqrt = square root)

1) In Dr Collin's packet it says cot 60* = 1/sqrt(3) = sqrt(3)/3
I don't understand why one over the square root of 3 is equal to square root of three over three?

2) also in Dr Collin's it says to find the sec of 45*. So sec is 1/cosine and the cos of 45* = sqrt(2)/2 so sec should be 2/sqrt(2) but the answer he gives is just sqrt(2). so I guess that's implying 2/sqrt(2) is equal to sqrt(2), and I don't understand why that is?

I feel like I used to know this but I haven't done this stuff since high school haha. I tried to reason it out but it's not working for me 😕

 

[UyenRita]

1) In Dr Collin's packet it says cot 60* = 1/sqrt(3) = sqrt(3)/3
I don't understand why one over the square root of 3 is equal to square root of three over three?

Multiply both denominator and nominator by sqrt of 3, you will get sqrt(3)/3 from 1/sqrt(3).

2) also in Dr Collin's it says to find the sec of 45*. So sec is 1/cosine and the cos of 45* = sqrt(2)/2 so sec should be 2/sqrt(2) but the answer he gives is just sqrt(2). so I guess that's implying 2/sqrt(2) is equal to sqrt(2), and I don't understand why that is?

Same thing as above. 2 = sqrt(2) x sqrt(2) . Then you cancel sqrt(2) from denominator and nominator. So you'll get sqrt(2) left in the nominator.

Make sense?

Good luck!

 

[philapharm7]

Multiply both denominator and nominator by sqrt of 3, you will get sqrt(3)/3 from 1/sqrt(3).



Same thing as above. 2 = sqrt(2) x sqrt(2) . Then you cancel sqrt(2) from denominator and nominator. So you'll get sqrt(2) left in the nominator.

Make sense?

Good luck!

THANK YOU SOOOO MUCH!!! you are my favorite person in the world right now! and yes that makes perfect sense!! as soon as I read it I remembered all that stuff from trig haha.
Okay so I understand why they are equal, and if I remember correctly you do that because you don't want a radical in the denominator. But is the radical-in-denominator form still technically correct? As in, if one of the multiple choice options was 1/sqrt(3) and sqrt(3)/3 was NOT an option, should I pick 1/sqrt(3)? Or is that not an acceptable form, and I should therefore assume I made a mistake somewhere?

 

[UyenRita]

THANK YOU SOOOO MUCH!!! you are my favorite person in the world right now! and yes that makes perfect sense!! as soon as I read it I remembered all that stuff from trig haha.
Okay so I understand why they are equal, and if I remember correctly you do that because you don't want a radical in the denominator. But is the radical-in-denominator form still technically correct? As in, if one of the multiple choice options was 1/sqrt(3) and sqrt(3)/3 was NOT an option, should I pick 1/sqrt(3)? Or is that not an acceptable form, and I should therefore assume I made a mistake somewhere?

Oh my goodness, for a very first time, I am now a favorite person of somebody. 😍

Yes, that would be acceptable, nothing is wrong with it.