Period of `sin theta - sqrt2 cos theta` is

Options

A. `pi/4`
B. `pi/2`
C. `pi`
D. `2pi`

Answer

To find the period of the function \( f(\theta) = \sin \theta - \sqrt{2} \cos \theta \), we can follow these steps:

### Step 1: Identify the periods of the individual trigonometric functions
The period of \( \sin \theta \) is \( 2\pi \) and the period of \( \cos \theta \) is also \( 2\pi \).

### Step 2: Determine the period of the combined function
Since both \( \sin \theta \) and \( \cos \theta \) have the same period of \( 2\pi \), the period of the function \( f(\theta) = \sin \theta - \sqrt{2} \cos \theta \) will also be \( 2\pi \).

### Step 3: Conclusion
Thus, the period of the function \( \sin \theta - \sqrt{2} \cos \theta \) is \( 2\pi \).

### Final Answer
The period of \( \sin \theta - \sqrt{2} \cos \theta \) is \( 2\pi \).

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