Damn instructors

Okay I have a horrible instructor. I need help with these practice problems

For trigonometry

"Find the general solutions of the eqasions algebraically"
(^2 is squared)
a. ( 4sin^2 x = 2cosx+1
b. sec(4x) =2

Thanks for any help.

sec4x=2
sec4=2/x
0.999990480720735= 2/x
0.999990480720735x=2
x=0.499995240360367

That's a bunch of bullcrap. I don't know how to do this.

>>2
haha oh wow

>>2
rofl

>>1
Ok, for the first one replace 4*sin^2(x) with 4*(1 - cos^2(x)), then you get 4 - 4cos^2(x) = 2cos(x) + 1, or 4cos^2(x) + 2cos(x) - 3 = 0. Let u = cos(x), then this is 4u^2 + 2u - 3 = 0. Solve for u using the quadratic formula, and then use cos^-1 on those solutions to get solutions for x.

Second one: sec(4x) = 2, so 1/cos(4x) = 2, so cos(4x) = 1/2, so 4x = (pi/3) + 2n*pi or (-pi/3) + 2n*pi, and x = (pi/12) + n/2 * pi or (-pi/12) + n/2 * pi.
(n is any integer)

(^2 is squared).

^5 is high five

(^2 is squared).

/sci/ is not your answer sheet.

>>1

Learn how to do this crap yourself.  Otherwise you're just contributing to the willful idiocy us TAs have to fight against when you get to college.

>>9

He's trying to learn it.  He said he had a horrible instructor, so he came here for help (which was a mistake on his part).  But you all get off on the fact that you've passed Calc 2, and you want to ensure that as few people as possible attain (and surpass) your mediocrity. That way you can continue lording it over them.

>>10
You tell 'im, Joe

search wikipedia, there are a set of rules for that (unfortunately i can't think of any right now, it's been a long time since i last solved (or rather attempted to solve) one of them. but what could help you (A would be x in your case):

sin(2A) = 2*sin(A)*cos(A)
cos(2A) = 2^cos(A) - 2^sin(A)
tan(2A) = (2*tan(A))/(1-2^tan(A)

It's basically a riddle game :) Feel free to use all kinds of trickery

>>4
Has it right.

The first one was a bit tricky, because of the quadratic formula.

The second one was pretty basic, using the definition of secant.

its 4.98715456^3

Use the trigometric identities noob.