Prove that sin x < x for x > 0

Thread starter stevenchan
Start date Jun 1, 2009
Tags

Sin

In summary, the notation "sin x < x" means that the value of sine of x is always less than the value of x for any value of x greater than 0. This inequality can be proven using the basic properties of sine and the properties of limits in calculus. Proving that sin x < x for x > 0 is important because it is a fundamental result in calculus and trigonometry, and is used in many other mathematical concepts and applications. For example, if we take x = 1, then sin 1 ≈ 0.84 which is less than 1, showing that sin x < x for x > 0. This inequality holds true for all values of x greater than 0 and has

Jun 1, 2009

stevenchan

Anyone knows how to prove it using Taylor's theorem?

Physics news on Phys.org

Jun 1, 2009

Cyosis

Homework Helper

Calculate the Taylor series of sin x and then take a close look at the alternating terms.

FAQ: Prove that sin x < x for x > 0

1. What does "sin x < x" mean?

The notation "sin x < x" means that the value of sine of x is always less than the value of x for any value of x greater than 0.

2. How can we prove that sin x < x for x > 0?

This inequality can be proven using the basic properties of sine and the properties of limits in calculus.

3. Why is this inequality important in mathematics?

Proving that sin x < x for x > 0 is important because it is a fundamental result in calculus and trigonometry. It is also used in many other mathematical concepts and applications.

4. Can you provide an example to illustrate this inequality?

For example, if we take x = 1, then sin 1 ≈ 0.84 which is less than 1. This shows that sin x < x for x > 0.

5. Is this inequality true for all values of x?

Yes, this inequality holds true for all values of x greater than 0. It is a fundamental result in mathematics and has been proven to hold for all values of x.