Why are cos (π) and cos (-π) both equal to -1?

Solution:

In trigonometry, cosine is an angle complementary to a sine angle. It is defined as a ratio of adjacent (base) sides to the hypotenuse.

As we know that, cos(π) = cos 180º

cos 180º lies in the second quadrant where cos has a negative value.

Therefore, cos (π) or cos 180º =  -1

By using trigonometry identity, cos(-θ) = cos(θ) 

So, cos(-π) = cos(π)  = -1 

Thus, the value of cos(π) and cos(-π) is equal to - 1.

Why are cos (π) and cos (-π) both equal to -1?

Summary:

π is 180º and using the identity, cos(-θ) = cos (θ) , the value of cos (π) and cos (-π) are equal.