Question

find the coordinates of a point on a circle with radius 5 corresponding to an angle of 335°. (x,y) = ( enter an integer or decimal number more... ) round your answers to three decimal places. question help: post to forum submit question

Explanation:

Step1: Recall polar - to - rectangular conversion formulas

The conversion from polar coordinates $(r,\theta)$ to rectangular coordinates $(x,y)$ is given by $x = r\cos\theta$ and $y = r\sin\theta$. Here, $r = 5$ and $\theta=335^{\circ}$.

Step2: Convert the angle to radians (optional but useful for some calculators)

We know that $1^{\circ}=\frac{\pi}{180}$ radians. So, $\theta = 335^{\circ}=335\times\frac{\pi}{180}=\frac{67\pi}{36}$ radians. But we can also directly use the degree - mode on a calculator.

Step3: Calculate the x - coordinate

$x = r\cos\theta=5\cos(335^{\circ})$. Since $\cos(335^{\circ})=\cos(360^{\circ}- 25^{\circ})=\cos(25^{\circ})\approx0.906$. So, $x = 5\times0.906 = 4.530$.

Step4: Calculate the y - coordinate

$y = r\sin\theta=5\sin(335^{\circ})$. Since $\sin(335^{\circ})=\sin(360^{\circ}-25^{\circ})=-\sin(25^{\circ})\approx - 0.423$. So, $y = 5\times(-0.423)=-2.115$.

Answer:

$(4.530, - 2.115)$