Cos x=-1 Cos x=1

To solve the equations \( \cos x = -1 \) and \( \cos x = 1 \), we need to look for the angles \( x \) that satisfy these conditions within the context of the cosine function.

1. For \( \cos x = -1 \): The cosine function equals -1 at specific angles: \[ x = \pi + 2k\pi, \quad k \in \mathbb{Z} \] This means that \( x \) can be \( \pi, 3\pi, 5\pi, \) etc., or more generally, \( x = \pi + 2k\pi \) for any integer \( k \).

2. For \( \cos x = 1 \): The cosine function equals 1 at other specific angles: \[ x = 2k\pi, \quad k \in \mathbb{Z} \] This means that \( x \) can be \( 0, 2\pi, 4\pi, \) etc., or more generally, \( x = 2k\pi \) for any integer \( k \).

In summary:

• For \( \cos x = -1 \): \( x = \pi + 2k\pi \) where \( k \) is an integer.
• For \( \cos x = 1 \): \( x = 2k\pi \) where \( k \) is an integer.