# If sin=0.4, what is sin(-theta) + csc theta?

May 26, 2016

$\setminus \sin \left(- \setminus \theta\right) + \setminus \csc \left(\setminus \theta\right) = - 0.4 + 2.5 = 2.1$

#### Explanation:

We have

$\setminus \sin \left(- \setminus \theta\right) = - \sin \left(\setminus \theta\right)$ because sine is an odd function

$\setminus \csc \left(\setminus \theta\right) = \frac{1}{\setminus} \sin \left(\setminus \theta\right)$ from the definition of the cosecant function