need help with this trig equation

[abel muroi]

I was given this problem.. cos x + 1 = 0 and was told to find all solutions of the equation.

here is my work...


cos x + 1 = 0
cos x = -1
x = 180 degrees


i double checked my work by "plugging in" 180 degrees for x (which is the same as -1) so i guess this is correct.

did i do anything wrong?

 

[Deleted member 4993]

I was given this problem.. cos x + 1 = 0 and was told to find all solutions of the equation.

here is my work...


cos x + 1 = 0
cos x = -1
x = 180 degrees


i double checked my work by "plugging in" 180 degrees for x (which is the same as -1) so i guess this is correct.

did i do anything wrong?

That is one of the solutions. However,

cos(180+360) = -1

cos(180+720) = -1

cos(180-360) = -1 ..... and so on

General solution is:

cos[(2*k ±1)* π)] = -1 where k = any integer

 

[abel muroi]

That is one of the solutions. However,

cos(180+360) = -1

cos(180+720) = -1

cos(180-360) = -1 ..... and so on

General solution is:

cos[(2*k ±1)* π)] = -1 where k = any integer

if i am told that my solution must be within the range of 0 and 360... does that mean that the only solution to this problem is 180?

 

[Steven G]

if i am told that my solution must be within the range of 0 and 360... does that mean that the only solution to this problem is 180?

Yes. My concern is that in your previous post you said that 180 is the same as -1. Since -1+1=0, is 180 + 1=0?? Be precise!

 

[abel muroi]

Yes. My concern is that in your previous post you said that 180 is the same as -1. Since -1+1=0, is 180 + 1=0?? Be precise!

i have one more question, is there a general formula for finding all solutions to a trig equation?

 

[Steven G]

i have one more question, is there a general formula for finding all solutions to a trig equation?

Each trig function has a period length. Find ALL the solutions within one period and then add n*period for each solution you found where n=0,=/-1, +/-2,---. For example if you found x1 and x2 are all the solutions in one period and the length of a period is k, then the solution will be x1 +nk and x2+nk for n=0, +/-1, +/-2, +/-3...