Trignometric simple function:-

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Discussion Overview

The discussion revolves around the properties and implications of the tangent function, particularly focusing on the concept of negative angles and their representation in trigonometry. Participants explore the domain of the tangent function, the nature of negative angles, and the significance of negative values in trigonometric functions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the inclusion of integers in the domain of the tangent function, suggesting that natural numbers might be more appropriate, while expressing skepticism about negative angles.
  • Another participant asserts that negative angles are valid and that trigonometric functions extend infinitely in both positive and negative directions.
  • Several participants request examples of negative angles using the tangent function, specifically asking for calculations involving the angle -45 degrees.
  • There is a discussion about how the tangent of an angle can be negative, with references to the geometric interpretation of angles and their direction based on rotation.
  • Participants explore the meaning of the negative sign in the context of tangent values and how it relates to the physical representation of angles.
  • Questions arise regarding the role of quadrants in representing direction and the purpose of negative axes in graphs, with one participant suggesting that negative numbers are as valid as positive numbers.

Areas of Agreement / Disagreement

Participants express differing views on the nature of negative angles and their implications in trigonometry. While some acknowledge the existence of negative angles, others question their relevance or understanding. The discussion remains unresolved regarding the appropriateness of integers versus natural numbers in the context of the tangent function's domain.

Contextual Notes

There are unresolved assumptions about the definitions of angles and the implications of negative values in trigonometric functions. The discussion does not clarify the mathematical steps involved in determining the domain of the tangent function.

Huygen121
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Can you please tell me the reason behind this relation:-

y=tanx

Domain:-

R-{(n*180) + 180/2),n ε Z(integers))}

but how can n belong to integer because if n belong to integer than an angle would be negative and i don't think so that negative angles are there,i think that in place of (integers),natural nos. should come.but why they don't put natural nos. in place of integers,there??
 
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Of course there are negative angles. All trig functions extend infinitely in the positive and negative directions.
 
can you give me an example related to it by just using the tan x and putting value in it?
 
can the tan of an angle be negative,if so,then how?
 
Huygen121 said:
can you give me an example related to it by just using the tan x and putting value in it?

You can use a calculator. Select degree mode if needed. Input -45. Press TAN. The result should be -1.

Physically, this would correspond to pointing your arm at an object that is 100 feet away horizontally and 100 feet down vertically. The angle is 45 degrees below horizontal and the tangent of the angle is the result of dividing the opposite side (-100 feet vertical) by the adjacent side (100 feet horizontal).
 
jbriggs444 said:
You can use a calculator. Select degree mode if needed. Input -45. Press TAN. The result should be -1.

Physically, this would correspond to pointing your arm at an object that is 100 feet away horizontally and 100 feet down vertically. The angle is 45 degrees below horizontal and the tangent of the angle is the result of dividing the opposite side (-100 feet vertical) by the adjacent side (100 feet horizontal).

but what exactly (-) minus sign indicates as we know dimensions are same to + angle ?
 
Huygen121 said:
can the tan of an angle be negative,if so,then how?
Because an angle can be negative. An angle is defined by two rays that extend from a common point. In mathematics, the starting ray usually extends out along the x-axis. If you rotate a terminal ray counterclockwise, you get a positive angle. If you rotate the terminal ray clockwise, you get a negative angle.
 
Mark44 said:
Because an angle can be negative. An angle is defined by two rays that extend from a common point. In mathematics, the starting ray usually extends out along the x-axis. If you rotate a terminal ray counterclockwise, you get a positive angle. If you rotate the terminal ray clockwise, you get a negative angle.


can quadrants represent direction?
 
what is the use of negative axis in graph? simple question and it will clear my all doubts
 
  • #10
Huygen121 said:
what is the use of negative axis in graph? simple question and it will clear my all doubts

It sounds as though you have a problem with negative numbers in general. The negative axis on a graph is there because negative numbers exist as much as the positive numbers exist.
 

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