Inverse Cosine Function (1 Viewer)

frog1944

Member
Joined
Apr 9, 2016
Messages
210
Gender
Undisclosed
HSC
2017
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
 

frog1944

Member
Joined
Apr 9, 2016
Messages
210
Gender
Undisclosed
HSC
2017
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

Well-Known Member
Joined
Apr 28, 2015
Messages
464
Gender
Undisclosed
HSC
2015
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).
 
Last edited:

frog1944

Member
Joined
Apr 9, 2016
Messages
210
Gender
Undisclosed
HSC
2017
Ok, so I think the simplified version for sinx=0 is x=pi/2 +2kpi, is that correct?
 

fluffchuck

Active Member
Joined
Apr 29, 2016
Messages
239
Location
Sydney
Gender
Male
HSC
2017
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

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
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).
 
Last edited:

frog1944

Member
Joined
Apr 9, 2016
Messages
210
Gender
Undisclosed
HSC
2017
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

Member
Joined
Apr 9, 2016
Messages
210
Gender
Undisclosed
HSC
2017
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.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top