Page:Calculus Made Easy.pdf/185

CHAPTER XV.

HOW TO DEAL WITH SINES AND COSINES.

Greek letters being usual to denote angles, we will take as the usual letter for any variable angle the letter $\theta$ (“theta”).

Let us consider the function

$y=\sin \theta$.

Fig. 43.

What we have to investigate is the value of ${\frac {d(\sin \theta )}{d\theta }}$; or, in other words, if the angle $\theta$ varies, we have to find the relation between the increment of the sine and the increment of the angle, both increments being indefinitely small in themselves. Examine Fig. 43, wherein, if the radius of the circle is unity, the height of $y$ is the sine, and $\theta$ is the angle. Now, if $\theta$ is