Question

Find the General value of theta,when cos (-theta/2) =0​

Answer 1

Answer:

The basic graph of y = cos(x) just has real x values and real y values.

The key to understanding my answer is that we can find some complex values of x which still produce real y values!

In order to allow complex x values, I need to write the x values as complex numbers so I will replace x with x + iz

Instead of just y = cos(x), I will use y = cos(x + iz)

Obviously I will need a real x axis and an imaginary x axis which I called z.

let y = cos(x + iz)

= cos(x) cos(iz) + sin(x) sin(iz)

= cos(x) cosh(z) + isin(x) sinh(z)

I know this looks awful but notice that certain values of x will ensure that the y values stay real.

If x = 2nπ ie 0, 2π, 4π ….

Then y = cos(2nπ)×sinh(z)

so that y = +1×cosh(z) + i×0 = cosh(z)

In fact for all values of x = 2nπ then y = cosh(z)

Also if x = (2n+ 1)

Then y = –1×cosh(z) + i×0 = – cosh(z)

Step-by-step explanation: