# Solving a trigonometric equation

• Dec 3rd 2012, 08:18 AM
Lethargic
Solving a trigonometric equation
Solve on the domain 0° ≦ x ≦ 360°. Use a calculator and round to the nearest degree if unable to use special triangles.

cos x-1 = -cos x

Can anyone give me some pointers on this one? I'm taking grade 12 math through an independent learning course, where I have no access to a teacher, and this question has me completely stuck.

I've solved other trig equations by isolating x and using a special triangle, a calculator, or simply looking at the graph sometimes. However, the right side of the equation has always been a real number in the past, and I'm not sure what to do with this -cos x.
• Dec 3rd 2012, 08:25 AM
coolge
Re: Solving a trigonometric equation
Is it cos (x) - 1 or cos(x-1)?
• Dec 3rd 2012, 08:26 AM
Lethargic
Re: Solving a trigonometric equation
It is cos x - 1

No brackets written whatsoever
• Dec 3rd 2012, 08:31 AM
coolge
Re: Solving a trigonometric equation
If it is cos x - 1 = -cos x
then 2cos x = 1
cos x = 1/2
x = phi/3 and 5 phi/3
• Dec 3rd 2012, 08:35 AM
Lethargic
Re: Solving a trigonometric equation
Thanks! I was over-thinking that far too much
• Dec 3rd 2012, 08:35 AM
Plato
Re: Solving a trigonometric equation
Quote:

Originally Posted by Lethargic
It is cos x - 1
No brackets written whatsoever

Please learn to use correct notation. The cosine is a function and as such it should be written in function notation: $\cos(x)$.
You would not write $f\,x$ for $f(x)$, would you?
• Dec 3rd 2012, 08:46 AM
Lethargic
Re: Solving a trigonometric equation
Tell that to whomever wrote my textbook
• Dec 3rd 2012, 11:47 AM
skeeter
Re: Solving a trigonometric equation
Quote:

Originally Posted by coolge
If it is cos x - 1 = -cos x
then 2cos x = 1
cos x = 1/2
x = pi/3 and 5 pi/3

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