Derivative of sine, geometric proof
<p>The right-angled triangle <strong>OPA</strong> has an angle θ 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 <strong>AP</strong> as <em>y</em>. Since <strong>OA</strong> is the radius of a unit circle, it is 1. So the sine of <em>θ</em> is simply:</p>
<p>While we are looking at this diagram, it is also worth noting that the arc of the circle between <strong>X</strong> and <strong>A</strong> has a length <em>θ</em>. That is because the arc subtends an angle <em>θ</em> at the centre of the circle. The length of an arc is given by <em>rθ</em> (provided <em>θ</em> is measured in radians), and since <em>r</em> is 1 for a unit circle, the length is simply <em>θ</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>