Math help!! URGENT

So I've got a makeup test to turn in tomorrow, and I need help with a few questions. I'd post in the homework help section, but apparently, I don't have the permissions to...(?)

Anyway, here's the problems, if you can solve any or all of them, I'd greatly appreciate it!

Find all solutions of the given equations:

#1:
2cos²x-cosx-1=0
After using the quadratic equation, I come up with cosx=1 OR -1/2
What do I do next?


#2:
cos5t=1/2
No idea what to do with this :[

 

cos(x) = 1,-1/2

If you have calculator
use inverse cos on on both sides (cos^-1) and solve.

If you don't, you have three ways. Unit circle and logic, memorization, or method of 30 60 90 and 45 45 90 triangles. Since you're in a hurry, looks like you'll need memorization.

http://www.mathplusfun.com/Content/Guide/Trigonometry/tri3b.gif

 

in the first question take : cosx as t.
so it becomes t.t.x.x+tx-1 ,,
use quadratic formula :
x= -b+rootD upon 2a and
x= -b - rootD upon 2a,

where a=t.t
b=t
c=1
D= b.b-4ac
when u"ll get 2 vales substitute t and u"ll get the answer

in second question we know that,
cos60=1/2
we are given,
cos5t=1/2

5t=60
so, t is 20degrees ,

thx , if i could help

 

If 5t=60, then t=12 not 20. Probably a typo incase you didn't catch it.

If they ask for all values of that satisfy that with no given range then the answer would look like

(degrees) + kpi, where k is any integer.

This varies from each trig function, not even sure if just pi is even right for any one of though.

 

I solved it, thanks for the help broskis! :]

 

lol, your funny, congratulations