How to Establish the Inequality xcosx < sinx < x Using the Unit Circle?

theperthvan
Messages
182
Reaction score
0
This was an exam question I had at the end of 2005 in my uni entrance exams.
Can you do it?

Establish the inequality

xcosx &lt; sinx &lt; x where 0&lt;x&lt;pi/2 using the unit circle.

is the tex working?
 
Mathematics news on Phys.org
This is a classic. Here:

http://www.csun.edu/~ac53971/courses/math350/xtra_sine.pdf"

The first part of the proof is what you are looking for.

Edit: Is it a challenge? If so then most people here will be able to do it, this is a very known proof.
 
Last edited by a moderator:
That was quick!

Yes, that's it. Cheers,
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

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...
View full post »

Thread 'Fermat's Last Theorem'

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...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

I Equation to graph a sine wave that acts like a point on a unit circle
Replies
8
Views
2K
MHB Approximating Trig Values using the Unit Circle
Replies
11
Views
3K
MHB How Much Should the Radius Increase to Enlarge the Circle's Area by b Units?
Replies
4
Views
2K
I Eccentric anomaly of ellipse-circle intersections
Replies
4
Views
2K
B Unit Circle and Other Trig Questions
Replies
10
Views
2K
I Family of Circles at Two Points
Replies
2
Views
2K
I Integrating Sin(x): Solve the Area of a Half Circle
Replies
2
Views
1K
B To calculate the polar unit vectors using rotated coordinates
Replies
1
Views
2K
MHB [ASK] Tangent of a Circle (Again)
Replies
2
Views
2K
MHB Find the exact shaded area of the region in 4 overlapping circles
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top