# I do not understand why i keep getting these trig equations wrong =(

1. Nov 2, 2009

### sportsstar469

cosx= -1/2 i realized my ref triangle is pie /6. i know that cosine is negative in quad 2 and 3. i labeled my axis (this helped me) with pie being 6 pie over 6, pie over 2 i put 3 pie over 6, 3pie over 2 i put as 9 pie over 6, and 2 pie i made 12 pie over 6.

ok since one solution is in quad 2(between 3 pie/6 and 6 pie/6) and ref angle is pie/6 i got 5pie/6

my other solution which is correct in the book is 4pie/3. so i got 4pie/3 and 5pie/6.

the book says 2pie/3 and 4 pie/3.

im just so frustrated, i thought i understood this stuff. its bad enough i cant understand, transformations, reflections, stretching, and compressing trig graphs, but now i cant do the equations either =(

those are my particulars not my general with periods./

i then did tanx= -1 and i got 3pie/4 and 7pie/4 as my answers. or since you just need one i just got 3pie/4 + pie k/. the book says the answer is -pie over 4.

2. Nov 2, 2009

### Tedjn

What angle gives cos x = 1/2? Is it pi/6?

3. Nov 2, 2009

### Staff: Mentor

???
The domain of the inverse tangent function (tan-1(x) or arctan(x)) is $-\pi/2 < x < \pi/2$, so that might be why your book gave an answer of $\pi/4$. The reference point for this angle is the same as the reference point for $7\pi/4$.

BTW, "pie" is something to eat. The name of this Greek letter, $\pi$, is pi.

Last edited: Nov 2, 2009
4. Nov 2, 2009

### sportsstar469

yes, i used the special triangle thats what i was told in class...

edit ITS PI OVER 3!!!!!! WOW I HATE MAKING STUPID MISTAKES!!!!!!!!!!!!

ANYBODY HAVE ANY TIPS ON (sorry caps) transforming graphs of sine and cosine i am totally lost here ;))
whyd you put questions under that part? their are general solutions and particular lol. the general is when you add the periods.

im not really sure what you were trying to say, but i think youre saying my second problem was ok?

i know the reference points are the same... when solving trig equations youre supposed to find the exact solutions.. do you remember how to do this

Last edited: Nov 2, 2009
5. Nov 2, 2009

### Staff: Mentor

I still don't know what you're talking about when you say "add the periods."
Maybe. Were you asked to find a solution in a certain interval? If you were asked to find a solution in the interval [$-\pi/2, \pi/2$], your answer of 7$\pi$/4 isn't in that interval. Keep in mind that the reference points are the same, but the angles aren't equal.
Yes, I remember how to do this, but what's your point?

6. Nov 2, 2009

### sportsstar469

these are from what i know, just basic level 1 trig equations. m supposed toi find the particular solutions (the exact angles from the ref angles (nott he ref angles) and then by general solution i mean i take my exact angles and add the period to it.
if my particular solution was 5pie over 3 for a sin equation my general would be that angle plus two pi k.