12.
$$y = \sin x$$
where \(x\) is measured in radians.
Use differentiation from first principles to show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \cos x$$
You may
- use without proof the formula for \(\sin ( A \pm B )\)
- assume that as \(h \rightarrow 0 , \frac { \sin h } { h } \rightarrow 1\) and \(\frac { \cos h - 1 } { h } \rightarrow 0\)