Question

find the coordinates of a point on a circle with radius 5 corresponding to an angle of 260°
(x,y) = ( , )
round your answers to three decimal places.
question help: video

Explanation:

Step1: Use the formula for coordinates on a circle

For a circle of radius \(r\) and angle \(\theta\) (in degrees), the coordinates \((x,y)\) are given by \(x = r\cos\theta\) and \(y = r\sin\theta\). Here \(r = 5\) and \(\theta=260^{\circ}\).

Step2: Calculate the \(x\) - coordinate

First, convert the angle to radians if using a calculator in radian mode (\(260^{\circ}=260\times\frac{\pi}{180}\text{ radians}\approx4.537856\text{ radians}\)). Then \(x = 5\cos(260^{\circ})\). Using a calculator, \(\cos(260^{\circ})\approx - 0.173648\), so \(x = 5\times(-0.173648)=-0.86824\approx - 0.868\).

Step3: Calculate the \(y\) - coordinate

\(y = 5\sin(260^{\circ})\). Using a calculator, \(\sin(260^{\circ})\approx - 0.984808\), so \(y = 5\times(-0.984808)=-4.92404\approx - 4.924\).

Answer:

\((x,y)=(-0.868,-4.924)\)