# Why Is My Integral Result Incorrect for Cosine of 2 Theta?

• PieOperator
In summary, the integral of cosine of 2 theta from pi minus theta1 to pi plus theta1 is equal to negative one half sine of 2 theta1. This is due to the incorrect vector orientation, which can be corrected by reversing the direction of the vector.
PieOperator

## Homework Statement

From angles pi minus theta1 to pi plus theta1, what is the integral of cosine of 2 theta times d theta?

## The Attempt at a Solution

When I evaluate this definite integral from pi minus theta1 to pi plus theta1, I get positive one half sine of 2 theta1.
It should be NEGATIVE one half sine of 2 theta1.

Is 2pi + 2theta1 and 2pi - 2theta1 somehow wrong?

Hi PieOperator!

(have a pi: π and a theta: θ and an integral: ∫ and try using the X2 tag just above the Reply box )

you should have got [1/2 sin2θ]π-θ1π+θ1

what happened then?

Thanks. I found my mistake. It has to do with vectors and the correct orientation. It is positive one half sine of 2 theta in the incorrect vector orientation. I just have to reverse the direction of the vector, and the interval reverses as well.

## What is the formula for cosine of 2 times theta?

The formula for cosine of 2 times theta is cos(2θ) = cos²θ - sin²θ.

## What is the range of values for cosine of 2 times theta?

The range of values for cosine of 2 times theta is between -1 and 1.

## What is the relationship between cosine of 2 times theta and cosine of theta?

The relationship between cosine of 2 times theta and cosine of theta is that cos(2θ) = 2cos²θ - 1.

## How can cosine of 2 times theta be used in real-world applications?

Cosine of 2 times theta can be used in real-world applications such as signal processing, sound and vibration analysis, and in the study of periodic phenomena.

## What is the geometric interpretation of cosine of 2 times theta?

The geometric interpretation of cosine of 2 times theta is the ratio of the adjacent side to the hypotenuse in a right triangle with an angle of 2θ.

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