Derivative of sine, geometric proof

<p>The right-angled triangle&nbsp;<strong>OPA</strong>&nbsp;has an angle &theta; at the centre of the circle. We can find the sine of the angle from the standard formula:</p> <p>We will represent the length&nbsp;<strong>AP</strong>&nbsp;as&nbsp;<em>y</em>. Since&nbsp;<strong>OA</strong>&nbsp;is the radius of a unit circle, it is 1. So the sine of&nbsp;<em>&theta;</em>&nbsp;is simply:</p> <p>While we are looking at this diagram, it is also worth noting that the arc of the circle between&nbsp;<strong>X</strong>&nbsp;and&nbsp;<strong>A</strong>&nbsp;has a length&nbsp;<em>&theta;</em>. That is because the arc subtends an angle&nbsp;<em>&theta;</em>&nbsp;at the centre of the circle. The length of an arc is given by&nbsp;<em>r&theta;</em>&nbsp;(provided&nbsp;<em>&theta;</em>&nbsp;is measured in radians), and since&nbsp;<em>r</em>&nbsp;is 1 for a unit circle, the length is simply&nbsp;<em>&theta;</em>. We will use this result later.</p> <p><a href="https://medium.com/recreational-maths/derivative-of-sine-geometric-proof-abf31e635eb1"><strong>Click Here</strong></a></p>