$\"\"$

The terminal side of the angle is in quadrant $\"\"$ .

Since the angle lies in quadrant $\"\"$ , $\"\"$ .

When the angle is doubled, $\"\"$ .

Rewrite the expression.

$\"\"$ .

Therefore, $\"\"$ lies in quadrant $\"\"$ and $\"\"$ .

When the angle is half, $\"\"$ .

Hence , $\"\"$ .

Therefore, $\"\"$ lies in quadrant $\"\"$ .

$\"\"$

$\"\"$ lies in quadrant $\"\"$ and $\"\"$ .

$\"\"$ lies in quadrant $\"\"$ .