Need explanation about sin rule

[MissP.25_5]

Hello.
This is part of a solution but I don't understand the underlined part. Why is it equals to 0?

 

[.Scott]

sin(wt)/6 x sin(2wt-(pi/4))
is not equal to zero.

 

[NascentOxygen]

Hello.
This is part of a solution but I don't understand the underlined part. Why is it equals to 0?

That term itself isn't zero. But the area under it, taken over the complete cycle 0→2 Pi contributes nothing to the integral that you are about to evaluate. So the author is just looking ahead and seeing that he can save himself a bit of work here, and not bothering to process a term that is going to end up as zero anyway.

Why don't you work through without dismissing that term, and see how the result pans out?

 

[D H]

An easy way to show that that term integrates to zero is to use the identity $\sin(a)\sin(b) = \frac 1 2 \bigl(\cos(a-b) - \cos(a+b)\bigr)$.

 

[rezeew]

Hello,
The sin rule, also known as the law of sines, is a mathematical rule that relates the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the opposite angle is equal to the ratio of the length of another side to the sine of its opposite angle. This can be written as a mathematical equation: a/sinA = b/sinB = c/sinC, where a, b, and c are the sides of the triangle and A, B, and C are the opposite angles. When solving for a missing side or angle in a triangle, we can use this rule to find the value.

In the underlined part, the value is equal to 0 because we are looking at a specific case where the angle is equal to 180 degrees. In this case, the sine of the angle would be equal to 0, and any number divided by 0 is undefined. Therefore, the value of the ratio would be 0.

I hope this helps to explain the sin rule better. Let me know if you have any further questions.