Express the following as functions of angles less than `45^(@)` :
`cos189^(@)`

Answer

To express \( \cos 189^\circ \) as a function of angles less than \( 45^\circ \), we can follow these steps:

### Step 1: Rewrite the angle
We can express \( 189^\circ \) in a different form that is easier to work with. We know that:
\[ 189^\circ = 180^\circ + 9^\circ \]

### Step 2: Use the cosine angle addition formula
Using the cosine of a sum identity, we have:
\[ \cos(180^\circ + \theta) = -\cos(\theta) \]
For our case, \( \theta = 9^\circ \):
\[ \cos(189^\circ) = \cos(180^\circ + 9^\circ) = -\cos(9^\circ) \]

### Step 3: Final expression
Thus, we can express \( \cos 189^\circ \) as:
\[ \cos 189^\circ = -\cos 9^\circ \]

This result is now expressed in terms of an angle less than \( 45^\circ \).

### Final Answer:
\[ \cos 189^\circ = -\cos 9^\circ \]

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