Inverse Cosine Function (1 Viewer)

[frog1944]

Hi,

Are the general solutions for cos(x) = cos(a), x = 2*pi*k +/- a (where k is an integer)? If so, I was trying to find the general solution to cosx = 0, I thought it would be 2*pi*k +/- pi/2, however there solution was pi/2 + k*pi. How did they get there solution?

Thanks

 

[kawaiipotato]

 

[frog1944]

Oh, ok. Yeah I do, I just didn't think of it like that, I was just substituting it into the formula (I'll have to think more carefully next time). For the cosx=1, is it 2*k*pi from the formula?

 

[kawaiipotato]

Oh yes, I meant there is a similar case for sinx = 0.
(Try and see the cases using the Unit Circle, it helps a lot).

 

[frog1944]

Ok, so I think the simplified version for sinx=0 is x=pi/2 +2kpi, is that correct?

 

[fluffchuck]

Ok, so I think the simplified version for sinx=0 is x=pi/2 +2kpi, is that correct?

No, for sinx=0, it is x=kpi.
I think you may have mistaken x=pi/2+2kpi as the general solution to sinx=1 (which is correct!)

 

[InteGrand]

I was trying to find the general solution to cosx = 0, I thought it would be 2*pi*k +/- pi/2, however there solution was pi/2 + k*pi.

Those two solution sets are the same (can you see why?).

Also, for finding the general solution for cos(x) (or other trig. functions) equal to some "special" values (basically 0 or ±1), it is usually easier to inspect the general solution from the graph rather using the general solution formula (the general solution formula will still give you the correct solution set, but it won't be in as "simplified" a form as it could be).

 

[frog1944]

No, for sinx=0, it is x=kpi.
I think you may have mistaken x=pi/2+2kpi as the general solution to sinx=1 (which is correct!)

You're correct fluffchuck, my bad, thanks for pointing it out .

 

[frog1944]

Those two solution sets are the same (can you see why?).

Yeah I think I can now see why they're the same, by your suggestion of looking at the graph. Awesome! Thank's Integrand, I'll keep in mind to look at the graph when they ask about general solutions to trigonometric functions.