Question

Find the coordinates of the point P at an angle of 45 degrees on a circle of radius 4.5. Round your answer to 3 decimal places. Enter a point as (a,b) including parenthesis.

Answer 1

$\bf sin(\theta)=\cfrac{y}{r} \qquad % cosine cos(\theta)=\cfrac{x}{r}\quad \begin{cases} r=radius=hypotenuse\\ x=adjacent\\ y=opposite\\ \theta=angle \end{cases}\\ -----------------------------\\ thus \\\\ \begin{cases} r=4.5\\ \theta=45^o \end{cases}\implies \begin{cases} sin(\theta)=\cfrac{y}{r}\to sin(45^o)=\cfrac{y}{4.5}\to 4.5\cdot sin(45^o)=y \\\\ cos(\theta)=\cfrac{x}{r}\to cos(45^o)=\cfrac{x}{4.5}\to 4.5\cdot cos(45^o)=x \end{cases} \\\\ P\ is \ at\quad (x,y)$

the angle is in degrees, thus, when taking either sine or cosine, make sure your calculator is in Degree mode