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

  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Trig Value
AI Thread Summary
To determine which trigonometric value is larger without a calculator, one can analyze the angle's quadrant. For an angle of 2 radians, which is approximately 114.6 degrees, it lies in the second quadrant where sine is positive and cosine is negative. Thus, it can be concluded that sin 2 is greater than cos 2. The discussion highlights the importance of understanding the unit circle and quadrants in trigonometry. Additionally, the user reflects on their educational experience and plans to study trigonometry more thoroughly.
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.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Back
Top