# how to calculate point coordinates on a circle and direction in degrees

In the image below, how can I calculate new point coordinate and direction which are marked in red text. The distance=$$1$$, radius=$$2$$ and angle=$$30$$ degrees. I tried to use the formula $$r\sin\theta$$ and $$r\cos\theta$$ but the answer does not match. The answer should be for the new coordinates: $$(0.24, 0.96)$$ and the direction should be $$28.65$$ degrees. Please help me to find out how can I do it.

• Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments. – José Carlos Santos Sep 21 '18 at 8:57
• I think i already gave a little idea that i tried rsinθ and rcosθ formula for calculating new point coordinates but i am unable to find any formula to find new direction in degree.In both cases my result is wrong – K.Malu Sep 21 '18 at 9:07
• How is the angle $30^{\circ}$? It should $\frac 12$ radians$\neq 30^{\circ}$ – Mohammad Zuhair Khan Sep 21 '18 at 9:17
• @MohammadZuhairKhan the steering angle is 30 degree. Turn radius for that steering angle is 2 which is also the radius of the circle. How are you saying the angle is 1/2 radians? I did not understand. – K.Malu Sep 21 '18 at 10:26
• Your definition of axes is not clear. If you want $\theta=0$ for $(x,y)=(0,0)$ then your circle has equations $y=r\sin\theta$ and $x=r(1-\cos\theta)$. Your direction (as drawn on graph) is exactly $\theta$, so you have to solve for it, given $x,y$. – N74 Sep 21 '18 at 11:03