Thread: Another trigonometric equation problem

The question:
Find all solutions of cos(z) = cos(2)

My attempt:
cos(z) = cos(x)cosh(y) - isin(x)sinh(y) = cos(2)

So we need:
sin(x)sinh(y) = 0 [1]
cos(x)cosh(y) = cos(2) [2]

[1] is zero when or y = 0
Substitute into [2]:


Try just y = 0:
So cos(x)cosh(0) = cos(x) which we want to equal cos(2), thus

Try just
So

Case when k is odd:
cosh(y) = -cos(2)

Case when k is even:
cosh(y) = cos(2)

Therefore, y =

So,

But the solution is :/

What am I doing wrong? Thanks.

Originally Posted by Glitch

Try just So

We have



But



So, we only obtain solutions for y=0.