Number of possible solutons for cosx=a?

[yojoe]

Discuss how many solutions the equation cosx=a can have, assuming that we consider only x in the interval [0,2pi]. The answer depends on a, so consider different values of a, and explain your choices.

I'm thinking that these values will only include the upper hemisphere of the trig circle from 0 to pi because it is a cosine function. So is 9 the number of solutions that are possible?

 

[Matt]

If a = pi, then there is exactly one solution in the interval [0,2*pi].

For any other value of a in [-1,1], there are two solutions in the interval [0,2*pi].

 

[pka]

If a=pi then there is no solution!
But if −1<a≤1 then there are TWO solutions.
If a=−1 there is ONE solution.
If |a|>1 there are no solutions.

 

[rahian2k]

[deleted]

 

[pka]

rahian2k come on, are you fully awake?
Have you ever seen a number a such that |a|=−1?

 

[Matt]

If a=pi then there is no solution!

How did I miss that???

rahian2k come on, are you fully awake?
Have you ever seen a number a such that |a|=−1?

Except for pka, it doesn't look like any of us are awake today.

 

[Gene]

If a=-1 there is one.
If a=+1 there are two. 0 and 2pi.
Note the [ and ]