# depressed by degrees problem

• December 29th 2008, 12:09 PM
freddie
depressed by degrees problem
Hi, I am a complete green horn on trig and have bought a rather naff "Trigonometry for Dummies" book that is beyond me.

I do not accept I cannot learn it as this book is not written in a way I can understand so have ordered another title.

Anyway onto my problem!

The coordinate plain is on the iPhone which is 320 * 460

The circle centre (is this the origin) is 160, 230

I use these equations to get my distance from centre and the degrees that this distance represents around the inside of the circle.

kSlideCentreX = 160 and kSlideCentreY = 230

Code:

distanceFromCentre = sqrt(((currentPosition.x - kSlideCentreX ) * (currentPosition.x - kSlideCentreX)) - ((currentPosition.y - kSlideCentreY) * ( currentPosition.y - kSlideCentreY)));
this is how I get the slope

Code:

slope = (kSlideCentreY - currentPosition.y) / (kSlideCentreX - currentPosition.x);

Code:

atan(slope)

gives me the degrees ( but not fixed yet )

Code:

atan(slope) / kRadiansPerDegree
this is supposed to fix them to real degrees?

Code:

90 - ( atan(slope) / kRadiansPerDegree)
my problem is that any coords on the right of the circle run from 180 degrees at the top (12) to 0 at the bottom (6), and on the left side from 180 at the bottom (6) to 0 at the top (12).

I can understand and learn things as long as they are done so in a fashion my brain can grasp (Worried)

I am searching and searching but coming up blank probably due to not asking the right question or how to phrase it.

I would be very grateful if someone could point me in the right direction or if feeling very friendly and helpful tutor me through this problem so I can learn from it and expand?

in hope......

Thanks
• December 29th 2008, 02:24 PM
galactus
I am not sure what you're asking for. What is it you want to understand?.

How to convert from radians to degrees?.
• December 29th 2008, 02:48 PM
freddie
Hi, well starting from 12 to 3 I would expect to see 0 to 90 then from 3 to 6 90 to 180 from 6 to 9 180 to 270 and finally from 9 to 12 270 to 360.

But I get 180 to 90 to 0 to 90 to 180?

I don't understand why this is so ?

Tomorrow I am going to plot a circle on graph paper and draw a triangle in it to see if I can visualize the calculation of distance and subsequent angle to determine the degrees, but am struggling to understand.

Have spent a lot of time tonight trying to find a downloadable trig course for beginners!
• December 29th 2008, 02:59 PM
galactus
In most applications the origin is the positive x-axis and travels counterclockwise. Therefore, as you have it in terms of a clock face.
0 is at 3, 90 is at 12, 180 is at 9 and 270 is at 6. Then it goes around and 360 is at 3 again.

The first quadrant is 0 to 90, second quadrant is 90 to 180, third quadrant is 180 to 270, fourth quadrant is 270 to 360(or 0).

To find angles, use $x=rcos{\theta}$ to find the x-coordinate

$y=rsin{\theta}$ to find the y-coordinate.

$r=\sqrt{x^{2}+y^{2}}$, Pythagorean theorem.

For instance, x=1 and y=1. $r=\sqrt{1^{2}+1^{2}}=\sqrt{2}$

That is the length of the hypoteneuse of the triangle formed.

Now, that is 45 degrees or $\frac{\pi}{4}$ radians.

$x=\sqrt{2}sin(\frac{\pi}{4})=1, \;\ \sqrt{2}cos(\frac{\pi}{4})=1$

See?. We got the coordinates (1,1).

This is a little different than the diagram because I used x and y of 1.

If we use r=1 as in the unit circle, then $x=1\cdot sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$. Just as on the diagram.

Also, $y=1\cdot cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$.

To convert from radians to degrees, multiply by $\frac{180}{\pi}$

To convert from degrees to radians, multiply by $\frac{\pi}{180}$

I have posted a diagram of the unit circle so you can see. Those Books for Dummies are not the best to learn from.

Does that help a wee bit?.
• December 29th 2008, 03:15 PM
freddie
Yep it does help a see bit.

I understand the layout of the degrees and yep sure did drop the ball on that one LOL

I lost you on the finding the x a y equations but caught up again on the conversion to degrees from radians.

I would already have the x,y coords and would use the 3,4,5 rule to get the distance and use that for getting the degrees I think?

Do you know if the product at top of this page Trigonometry Solved would be of any help to me? I know jack about trig but must learn it fast for work!

Am trying to find. Course or book aimed at kids I suppose seeing as my knowledge of this is so poor!

Example I only found out tonight that sine = opposite / hyp!

See how little I know ? :(
• December 29th 2008, 03:24 PM
freddie
Am just Reading an interesting web site on unit circle!

As I did not know what this was either
• December 29th 2008, 03:30 PM
galactus
There are all sorts of things if you google.

We all have to start somewhere. I learned trig years back when I began surveying.

Here is a diagram of the triangle with its respective trig and what sides they represent.

Of course, if it is not a right triangle, then it gets more complicated.

Law of Sines, Law of Cosines and so forth come into play. Lots to learn.
• December 30th 2008, 11:33 AM
freddie
Could someone confirm my thoughts that the example I have seen is wrong hence my confusion please?

OK...I am told of a right triangle with a 30 degree angle an opposite length of 4 and an unknown hypotenuse.

so to find the length hypotenuse, lets call it 'a' the following applies:

sin x = opposite / hypotenuse

sin 30 = 4 / a

a sin 30 = 4

a = 4 / sin 30

4 sin 30 = 8

Now I understand sin 30 = 0.5 so applying this to the above we get

0.5 = 4 / a ( a is 8 )

a 0.5 = 4 ( a is 8 )

a = 4 / 0.5 ( a is 8 )

4 0.5 = 8 ( no it does not? 4 0.5 = 2)

Have I missed something or is this last line an incorrect example?