If cos of theta = - (1/6), what is the cos (-10pi-theta) ?

How can i solve this question?

- (1/6).

Step-by-step explanation:

The angle whose cosine is - 1/6 can be written as arccos (-1/6).

cos (-1/6) = cos (-2npi - arccos (-1/6) where n is an integer. The terminal angles are the same. When n = 5 we have cos (-10pi - arccos (-1/6).

So cos (-1/6) = cos (-10pi - arccos (-1/6))

and therefore cos (-10pi - arccos (-1/6) = - 1/6.

We can confirm this by using a scientific calculator.