What is a two term tangent and how am I supposed to calculate it?

In summary, the speaker was able to use the distance formula to calculate the magnitude of a vector by adding the (i) and (j) components from two vectors and taking the sums. However, they are now trying to determine the angle of the vector and have come across the "atan2" process, which is used to calculate direction. While attempting to replicate the solution of -166.51 degrees, the speaker could not get the same answer and is seeking clarification on how to use inverse tangent to find degrees in the positive since the slope is positive. They also mention difficulties with reading pictures and ask for help with typing the problem statement and their own calculations in LaTeX.
  • #1
F14
1
0
Homework Statement
determine the magnitude and direction of V
Relevant Equations
Please refer to the pictures
So, I was able to run some numbers and get a magnitude with what looks to be the distance formula. I was able to do that by first adding the (i) and(j) components from the two vectors and then taking the sums and running them through that distance formula. So far so good, but now I have to figure out the degrees of its angle.

I looked up the problem on Chegg study to see what others have done and that is when I noticed that this "atan2" process was being used to calculate the direction. I have never heard of a two-term tangent before and when I looked that up, I mostly just got references to Fortran and MatLab usage. In the solution, it states that it is -166.51 degrees. I could not replicate that answer when I tried to do it on my own. I tried inverse tan to get my degrees, but those figures were under 80 degrees and in the positive since the slope is positive.

Could I get some insight into this, please?
 

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  • #2
F14 said:
never heard of a two-term tangent before
The trouble with atan(y/x) is that it loses sign information in the x and y values. If both are positive then the angle is in the first quadrant, but if both negative it is 180 degrees around in the third quadrant. Providing x and y as separate parameters solves this.
 
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Likes Dale and DaveE
  • #3
Your pictures are very hard to read. Neither the problem statement nor your own calculations can be clearly seen without further editing: downloads, change of brightness, zooming etc.

Please type in both: problem statement + what you did by using LaTeX. Here you can find how it is done:
https://www.physicsforums.com/help/latexhelp/
 

Related to What is a two term tangent and how am I supposed to calculate it?

What is a two term tangent?

A two term tangent is a mathematical concept used to measure the slope or steepness of a curve at a specific point. It is represented by the ratio of the length of the opposite side to the length of the adjacent side in a right triangle formed by the tangent line and the x-axis.

How am I supposed to calculate a two term tangent?

To calculate a two term tangent, you need to know the coordinates of the point on the curve where you want to find the tangent. Then, you can use the formula tan(x) = (y2-y1)/(x2-x1) where x1 and y1 are the coordinates of the point and x2 and y2 are the coordinates of a nearby point on the curve.

Do I need any special tools or knowledge to calculate a two term tangent?

To calculate a two term tangent, you will need a basic understanding of trigonometric functions and how to use them to find the slope of a line. You may also need a calculator to help with the calculations.

Why is it important to calculate a two term tangent?

Calculating a two term tangent is important because it allows you to determine the slope of a curve at a specific point. This can be useful in many fields, such as physics, engineering, and economics, where understanding the rate of change is crucial.

Are there any limitations to using a two term tangent?

Yes, there are some limitations to using a two term tangent. First, it can only be used to find the slope at a single point on a curve. Additionally, it may not accurately represent the overall behavior of a curve if the curve is very steep or has sharp turns.

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