Why does the trig expression just disappear?

Thread starter adamaero
Start date Apr 1, 2018
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Expression Hall effect Trig

In summary, when simplifying an equation, the trig expression may disappear because it can be reduced using trigonometric identities or algebraic manipulation. It is possible for the expression to completely disappear, but it is important to check the validity of the simplified equation. Simplifying trig expressions is important to make equations easier to solve and understand. There are rules and techniques for simplifying trig expressions, such as using identities and algebraic manipulation.

Apr 1, 2018

adamaero

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3. Solution

Then the equations from part (A) are used--but why does the converted trig (1-cos(etc)) go away?
Does this have to do with the mean-squared bit?

Last edited: Apr 1, 2018

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Apr 1, 2018

kuruman

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It becomes 1 when you time-average over one period.$$\frac{\int_0^{2\pi}(1-\cos x)dx}{\int_0^{2\pi}dx}=1$$

1. Why does the trig expression disappear when simplifying an equation?

When simplifying an equation, the trig expression may disappear because it can be reduced to a simpler form using trigonometric identities or basic algebraic manipulation. This is often done to make the equation easier to solve or to eliminate unnecessary terms.

2. Is it possible for a trig expression to completely disappear in an equation?

Yes, it is possible for a trig expression to completely disappear in an equation. This can happen when the expression can be reduced to zero or when it is equivalent to another term in the equation. It is important to check the validity of the simplified equation to ensure that no important information has been lost.

3. Can a trig expression disappear without altering the value of the equation?

Yes, a trig expression can disappear without altering the value of the equation. This can happen when the expression is equivalent to another term in the equation or when it can be simplified to zero. In such cases, the value of the equation remains unchanged.

4. Why is it important to simplify trig expressions in an equation?

Simplifying trig expressions in an equation is important because it can help to make the equation easier to work with and solve. It can also help to identify patterns and relationships between different terms in the equation, making it easier to understand the problem at hand.

5. Are there any rules or techniques for simplifying trig expressions?

Yes, there are several rules and techniques for simplifying trig expressions. Some common ones include using trigonometric identities (such as the Pythagorean identities) and basic algebraic manipulation (such as factoring and expanding). It is important to practice and familiarize oneself with these techniques in order to effectively simplify trig expressions in equations.