Question

If $P(x,y)$ is a point on the standard unit circle and $\theta$ is the angle made by radius OP with the positive direction of the x-axis then, express $P(x,y)$ in terms of $\theta$.

Answer 1

If $P(x,y)$ is a point on standard unit circle and $\theta$ is the angle made by radius OP with positive direction of x-axis then express $p(x,y)$ in term of $\theta$.

From fig

$\cos \theta =\frac{x}{r}\Rightarrow x=r\cos \theta$

$\sin \theta =\frac{y}{r}\Rightarrow y=r\sin \theta$

So $p(x,y)=p(r\cos \theta ,r\sin \theta )$

since for unit circle $r=1$

$\therefore p(x,y)=p(\cos \theta ,\sin \theta )$

Which is the required expression of p in terms of $\theta$