```typescript
/** Returns the quotient of **a** divided by **b**. */
export function safeDivide(a: number, b: number): number {
  /**
   * @throws {Error} if divisor is exactly zero or non-finite.
   *              @throws {TypeError} if either argument is not a number.
   */
  if (typeof a !== 'number' || typeof b !== 'number') {
    throw new Error('Both arguments must be numbers');
  }

  if (!isFinite(a) || !isFinite(b)) {
    throw new Error('Both arguments must be finite numbers');
  }

  if (b === 0) {
    throw new Error('Cannot divide by zero');
  }

  return a / b;
}
```