Question

find the coordinates of the point on a circle centered at the origin with radius 4 corresponding to an angle of 135 degrees

Answer 1

The radius is given below as

`\begin{gathered} r=4 \\ \theta=135^0 \end{gathered}`

The equation of a circle is given below as

`x^2+y^2=r^2(passing\text{ throught the origin\rparen}`

By converting the polar coordinate to rectangular coordinates, we will have

`x=rcos\theta,y=r\sin\theta`

By substituting the values, we will have

`\begin{gathered} x=r\cos\theta \\ x=4\cos135 \\ x=4*-0.707 \\ x=-2.828 \end{gathered}`
`\begin{gathered} y=rsin\theta \\ r=4\sin135 \\ r=4*0.7071 \\ r=2.828 \end{gathered}`

Hence,

The coordinates of the point on a circle centered at the origin with radius 4 corresponding to an angle of 135 degrees is

`\Rightarrow(x,y)\Rightarrow(-2.828,2.828)`