Question

Marco wrote the equation below.

Cos ( -π /2) = cos ( 3π / 2)

Which statement best describes Marcos equation?

Answer 1

It is true, because the cosine function has a period of 2π

Explanation:

Since, the period of the cos function is 360° ( or 2π radians ), it holds the property of:

`Cos(\theta)=Cos(2\pi +\theta)`

Taking
`\theta` as
`-(\pi)/(2)`,
`(2\pi + \theta)` is equal to
`2\pi + (-(\pi)/(2))\\=2\pi - (\pi)/(2)\\=(4\pi-\pi)/(2)\\=(3\pi)/(2)`

The equation is true!

Note: The cos function is even function

Hence, the equation is true, because the cosine function has a period of 2π, NOT because the cosine function is ODD, which it is not!!