Rewriting $-\sin\theta+i\cos\theta$ and $-\sin\theta-i\cos\theta$ as complex exponentials

Question

I have found myself with the expression

$$ -\sin(\theta) + i \cos(\theta) $$

and

$$ -\sin(\theta) - i \cos(\theta) $$

I would like to simplify these ... presumably using Euler... but I can't figure out how.

The only forms I have ever uses are the standard $e^{ix} = \cos(\theta) + i \sin(\theta)$ and $e^{-ix} = \cos(\theta) - i \sin(\theta)$

After reading through the Wikipedia article, the only instance of such an expression is regarding proving the Euler formula via polar coordinates, https://en.wikipedia.org/wiki/Euler%27s_formula#Using_polar_coordinates

Answer 1

Hint Calculate $$e^{i(\theta+\pi/2)}$$

Answer 2

Hint. Multiply the expressions by $$1=\frac{i}{i}=-ii$$ like so $-iiE=-i(iE),$ where $E$ is some expression.