okay, so i have a problem which i have solved to a point, but i was wondering if someone could help clarify the steps for me? it is : cosx+1=1, and i changed it so it became cosx=0, but i'm not sure if i'm doing it correctly or if my steps are correct.Thanks!

Question

anonymous · Answer

cosx + 1= 1
        - 1   -1   ........  Subtract 1 from both sides
cox x = 0

whpalmer4 · Answer

Yes, that's a reasonable step, though we can't guarantee that what came before is correct...

anonymous · Answer

all that was given was cosx+1=0, with the interval [0,2pi), and to find the solutions. I reached this point, but I'm not sure where to go from there. :) Thanks for helping.

whpalmer4 · Answer

Wait, $$\cos x + 1 = 0$$ or $$\cos x + 1 = 1$$?

anonymous · Answer

whoops, my bad. it is supposed to be cosx+1=1, i should have been more careful,

anonymous · Answer

but the rest is acccurate

phi · Answer

do you know what the plot of cos(x) looks like between 0 and 2 pi ?

anonymous · Answer

I know that it makes a complete round of the unit circle, right?

phi · Answer

see http://www.mathsisfun.com/algebra/trig-sin-cos-tan-graphs.html scroll down to cos graph

anonymous · Answer

I see... so it is this one right http://www.mathsisfun.com/algebra/images/cosine-graph.gif

phi · Answer

yes.  now list the x's where cos(x) is 0

anonymous · Answer

I'm not sure, is it 1 and -1?

phi · Answer

put your finger on the "blue line"  (the cosine curve) and trace it until you reach the x-axis.  then look down to see what x value that is (between 0 and 2pi)

anonymous · Answer

oh, i see, it's -3pi/2,-pi/2, pi/2,3pi/2

anonymous · Answer

thank you

phi · Answer

yes, but they only want the values in the interval  [0,2pi)

the bracket [0   means from 0
the "close parens"  2 pi ) means up to but not including 2 pi

in this case, there are only the 2 values  pi/2 and 3pi/2

anonymous · Answer

These values are familiar, so do they both count as a solution?

phi · Answer

Familiar or not, they are the two places in the interval [0, 2pi) where cos(x) is 0

anonymous · Answer

okay, once the problem is solved, by using the cos graph to see where the values match up, thus giving the correct solution

anonymous · Answer

Thanks everyone! This really helped! Have a good day!

phi · Answer

yes.  But most people memorize the sin, cos and tan of a few special angles.

anonymous · Answer

That makes sense. If you don't mind my asking, what angles are these exactly, just so i know what to keep track of? If not, that's okay, you've helped me a lot already. :)

phi · Answer

The angles (in degrees) are 0, 30, 45, 60, and 90
(in radians  0, pi/6,  pi/3, pi/4, 2pi/3 and pi/2 )

  angle       sin        cos              tan
      0         0            1                 0
    30        ½          sqr(3)/2        1/sqr(3)
    45     sqr(2)/2   sqr(2)/2          1
     60    sqr(3)/2      ½                sqr(3)
     90         1              0              not defined

phi · Answer

or see http://regentsprep.org/Regents/math/algtrig/ATT1/trigANGLES.htm

anonymous · Answer

This is so helpful! Thank you for your time and effort!