# angles

1. ### Does transformation P:(r,theta) -> (x=rcos(theta), y=rsin(theta)) preserve angles?

Let P be a transformation from (r,theta) -> (x=rcos(theta), y=rsin(theta)) be a mapping from R^2 to R^2. 1. Does P preserve angles at the point r=2, theta = pi/4? 2. By what factor does the map P distort area at the point r=2, theta = pi/4? All I know so far is that P is a 2x2 matrix that...
2. ### relation between sides

how does one figure out the relation between sides- knowing only the angles. For example if one knew all the angles of a triangle how would one figure out that side A is 2X side b which is 1/2 the hypotonuse?
3. ### Angles and degrees question

Hello everyone, I'm busy studying for the SAT & have ran into a problem that I do not quite remember in Geometry from my freshman year. I know it's an easy one to solve, but I can't figure out where to start. Can I have a little guidance on this? : Regards, Lance
4. ### Exterior angles

In the diagram(please see attachment), the exterior angles of triangle ABC are <FAC, <ACD, <ECB, <CBI, <HBA and <BAG. What about the angles <, <DCE, <HBI, are they not exterior?
5. ### Proving - All the angles of a rectangle are right angles.

Hey Guys, I need some help trying to prove that all the angles of a rectangle are right angles. My teacher asks us to go in depth so we have to list a ton of reasons. So first let's have the Given Given: Rectangle ABCD with right angle A Reason: Given, & the it's also the definition of a...
6. ### Transformations that preserves the vector angles?

I read somewhere that normal transformations (hermitian, unitary, orthogonal, etc...) preserves the angles between vectors. but transformation is a function that operates on one vector, not two (T(v)=w), so what angle exactly are we talking about here?
7. ### Trigonometric Ratios of Allied angles

Prove that sin(90+theta)=sin(theta) without using trigonometric identity of sin(a+b). Prove it using circular system of coordinates.
8. ### (Practical)Calculating the time of day with angles relative to the position of thesun

Hey guys, I havent posted in some time and have recently taken a lot of my spare time to enjoy the great outdoors. My inquisitive nature has lead me to try to figure out a way to tell time using only a cammenga military compass, for those of you who dont know what it is it allows you to see...
9. ### Help! Angles and Clocks

How would I go about figuring this out? Mario was studying angles and wondered if during his math class the minute and hour hands of the clock formed a right angle. If his class meets from 6:00 P.M. to 6:50 P.M., is a right angle formed? If so, figure out to the nearest second when the hands...
10. ### Help! Operations of angles?

Perform each of the following operations: 1. 13o48'39" + 18o34'39" 2. 11o23' - 6o50' Express the following without decimals. 1. 0.1o 2. 15.87​o
11. ### How to find the difference between angles of two complex numbers

Hi I have two vectors represented as complex numbers and need to calculate angle between in most efficient way. This is for implementing in C. If I use tan-1 to take angles of both and subtract it will take a lot of processing power. So, please suggest me an efficient method for this. Thanks...
12. ### Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?

4tan(x) = 6 [ 2tan(x)/1 - tan2(x) ] Let tan(x) = a 4a (1 - a2) = 12a 1 - a2 = 12a/4a 1 - a2 = 3 therefore, a2 = -2 Which doesn't seem right? Help would be appreciated, the solutions are 0, pi and 2pi And how do people type in that math text??! Thanks in advance
13. ### Trouble finding reference angles with radians

I am having trouble finding reference angles with radians. For instance: #1) 33pi/4 #2) -23pi/6 How do I go about solving these?
14. ### Rotating Top: Euler Angles?

Hi all, I've just started studying the motion of a rigid heavy (i.e. with gravity) spinning top using Euler's angles. It mostly makes sense, but there's one point in my notes where we've derived the equations of motion using Euler-Lagrange and one of them is (theta, phi are the usual Euler...
15. ### Find Remaining Angles and Sides

Find remaining angles and side if they exist. If no triangle exists, say "No triangle" a=4 a=1 y=100 degrees (the problem does not state where angle y lies) please solve and explain process I am doing a similar problem but found this one in the book.
16. ### Obtaining Euler angles from two points

Hi, I have a problem. Essentially I have two points, which are centered about the origin but located arbitrarily in space otherwise. Basically I want to obtain the three Euler angles which transform my coordinates to a coordinate system where the points lie along the y' (transformed y) axis. It...
17. ### Find Remaining Angles and Sides of triangle

Find the remaining angles and side if they exist. If no triangle exists, say "No triangle" a= 4 b=1 y=100 degrees Please help!
18. ### Angles and pixels in a photo: Are trigonometric functions scale dependent?

In a photo each pixel represents an angle. In an image of two objects with known angle (e.g. two stars), one could count the number of pixels between them and determine the ratio pixels/angle degree of that camera for all other purposes. I try to ignore the true ratio and just use pixel as an...
19. ### Compound angles HELP!

Hi I'm new to this, I've been given a question on compound angles and I really don't know how to go about it. Any help would be greatly appreciated: Using compound angles prove that Cos(y-pi)+Sin(y+pi/2)=0 thanks Shaun
20. ### Rigid 3D matrix to Euler angles problem

Hello all, I'm working with 3D objects and I need to transform one into another space. To do so, I have the rigid 3D transformation matrix but I need the corresponding Euler angles because the software I use (and I must use this soft) only takes Euler angles as input. I did it successfully...