theres also this question that was answered but the solution ive found is very incorrect

**https://web2.0calc.com/questions/precal-help_1**

theres also a part two that came with the problem i would love to be helped with- but i dont wanna seem like im taking advantage of the site so you dont have to do it- but thank you so much for all your help :')

Say that \(\cos (\alpha) = 12/13\) and \(\cos (\beta) = -4/5\). Then if \begin{align*} T &= (t_1, t_2),\\ U &= (u_1, u_2), \end{align*}enter \(t_1, t_2, u_1, u_2\).

thanks sm in advance again :D

heartSTORM907 Sep 6, 2023

#3**0 **

This question is going to require a bit more clarification before someone can solve it definitively. The diagram on https://web2.0calc.com/questions/precal-help_1 is a bit odd because the question asker is looking for information about R and S, yet \(\alpha\) relates to the terminal point P and \(\beta\) relates to the terminal point Q. No information is given about the other terminal points. I could make some educated guesses, but I cannot prove that any of those guesses are justified. Are you sure there is not more information given somewhere? Either I am missing something or this question is nonsensical as written.

The3Mathketeers Sep 7, 2023

#4**0 **

Can you provide the missing information for this comment?

" and let R,S,T,U be the same as above:"

ElectricPavlov Sep 7, 2023

#6**+2 **

I believe that B - A = R and B + A = S

cos A = ( 12/13) sin A = (5/13) (A is a first quad angle)

cos B = (-4/5) sin B = (3/5) (B is a second quad angle)

cos ( B - A) = cos A cosB + sinAsinB = ( 12/13)(-4/5) + ( 5/13)(3/5) = [-48 + 15 ] / 65 = -33/65

So (x, y) = ( r1, r2)

r1 = -33 r2 = sqrt [ 65^2 - 33^2 ] = 56

So (r1, r2) = ( -33, 56)

Likewise

cos ( A + B) = cosAcosB - sinAsinB = (12/13) (-4/5) - (5/13)(3/5) = [-48 - 15] / 65 = -63/65

And again (x, y) = (s1, s2)

s1 = -63 s2 = sqrt ( 65^2 - 63^2) = 16

So

(s1,s2) = (-63 , 16)

CPhill Sep 7, 2023

#18**+1 **

Hello HeartStorm907

Before I start I will make it very clear that I have not looked at question or answer properly.

I will also say that I have NEVER said it is ok to post AoPS questions, especially when you are just looking for the answer.

Why do I think you are just after the answer?

Becasue you did not notice that originally key elements of the questin were missing.

AND more importantly

Because you just told CPhill his long answer was 'wrong'

It is easy to have a fundamentally correct answer but due to some small error somewhere the last line could be incorrect.

Did you look at CPhill's working? Or did you just plug in the last line and dismiss all he had done for you.

I never saw a thankyou anywhere. (for his time and effort)

Nor did I see you ask for any clarification of his working.

Melody
Sep 16, 2023