How can I determine the biggest trig value without a calculator?

  • Context: MHB 
  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Trig Value
Click For Summary

Discussion Overview

The discussion revolves around determining which trigonometric value is larger without the use of a calculator, specifically comparing values such as cos(2) and sin(2). The scope includes conceptual understanding of trigonometric functions and their properties in different quadrants.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asks how to determine which trigonometric value is larger without a calculator, using the example of cos(2) versus sin(2).
  • Another participant identifies that an angle of 2 radians is in the second quadrant, where cosine is negative and sine is positive.
  • Some participants suggest that since sine is positive and cosine is negative in the second quadrant, it can be concluded that sin(2) is greater than cos(2).
  • A later reply reiterates the quadrant analysis and supports the conclusion that sin(2) > cos(2) based on the properties of trigonometric functions in that quadrant.
  • One participant shares a personal experience about a lack of education on trigonometric concepts in their past coursework, expressing a desire to learn more through a specific textbook.

Areas of Agreement / Disagreement

There appears to be agreement among some participants regarding the relationship between sin(2) and cos(2) based on quadrant analysis, while the initial question about determining the largest trig value without a calculator remains open to further exploration.

Contextual Notes

Participants rely on quadrant properties and definitions of trigonometric functions, but there may be missing assumptions regarding the specific values of sin(2) and cos(2) that are not calculated or verified in the discussion.

mathdad
Messages
1,280
Reaction score
0
How do I determine which trig value is bigger or smaller without using a calculator?

Sample:

Which is bigger: cos 2 or sin 2?
 
Mathematics news on Phys.org
In which quadrant is an angle of 2 radians?
 
Angle 2 radians in degrees is 114.6°. We are in quadrant 2.

In quadrant 2, cosine is negative and sine is positive.

So, can I conclude by saying that sin 2 > cos 2?
 
RTCNTC said:
Angle 2 radians in degrees is 114.6°. We are in quadrant 2.

In quadrant 2, cosine is negative and sine is positive.

So, can I conclude by saying that sin 2 > cos 2?

Yes, we know the angle is in quadrant II since:

$$\frac{\pi}{2}<2<\pi$$

And so your result follows. :)
 
This is interesting. I took a course by the title Math 185 at NYC TECHNICAL COLLEGE in the early 1990s. The course covers Algebra 2 and Trig. The professor never introduced this material. In fact, he decided to skip the entire unit circle and how it works. I am going to use the David Cohen textbook to learn all the trig I missed in my youth. I AM A VICTIM OF NYC PUBLIC SCHOOL EDUCATION.
 

Similar threads

MHB How Can I Evaluate Trig Functions Without a Calculator?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad A Trick to Memorizing Trig Special Angle Values Table
  • · Replies 3 ·
Replies
3
Views
2K
High School Calculating trigonometry without calculator?
  • · Replies 8 ·
Replies
8
Views
2K
High School Brushing Up Math Knowledge: Basic Trig Questions
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Adding trig functions with different amplitudes
  • · Replies 5 ·
Replies
5
Views
2K
High School Why do we care about trig identities?
  • · Replies 17 ·
Replies
17
Views
6K
MHB Approximating Trig Values using the Unit Circle
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Is it possible to calculate this geometrical relationship between circles?
  • · Replies 7 ·
Replies
7
Views
2K
How to Determine Correct Inverse Trig Angle?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Finding the explicit solution of a trig equation
  • · Replies 6 ·
Replies
6
Views
2K