Differentiate the law of Cosine

In summary, the law of cosine is a mathematical formula used to relate the lengths of the sides of a triangle to one of its angles. It is different from the law of sine in that it is specifically used for non-right triangles. The formula for the law of cosine is c² = a² + b² - 2ab cos(C), and it has various real-life applications such as in navigation and surveying. Common mistakes when applying the law of cosine include using the wrong formula, misinterpreting angles, and using incorrect units. It is important to label angles and sides accurately and double-check calculations to avoid these errors.
  • #1
ryank614
10
0
It is a simple math question, but I am stuck.

The law of cosines is

R^2=h^2 + r^2 - 2 h r cos (theta). Theta is of course the angle facing R.

To differentiate, I first set

r^2 - 2hr cos[tex]\Theta[/tex]+ (h^2-R^2) = 0

2 r [tex]\dot{}r[/tex] - 2 h cos[tex]\Theta[/tex] [tex]\dot{}r[/tex] + (h^2-R^2) = 0.

Is there any way to put h^2-R^2 in terms of [tex]\dot{}\theta[/tex] or d[tex]\theta[/tex]/dt
 
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  • #2
Arr, nevermind. I got it.
 

What is the law of cosine?

The law of cosine, also known as the cosine rule, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is often used in trigonometry and geometry to solve for unknown side lengths or angles in a triangle.

How is the law of cosine different from the law of sine?

The law of cosine and the law of sine are both trigonometric laws used to solve for unknown sides and angles in a triangle. However, the law of cosine is specifically used for solving triangles that do not have a right angle, while the law of sine is used for right triangles.

What is the formula for the law of cosine?

The formula for the law of cosine is c² = a² + b² - 2ab cos(C), where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides of the triangle.

How is the law of cosine used in real life?

The law of cosine has many applications in real life, such as in navigation and surveying. For example, it can be used to determine the distance between two points on a map or the height of a building by measuring angles and side lengths.

What are some common mistakes when applying the law of cosine?

Some common mistakes when applying the law of cosine include using the wrong formula, misinterpreting angles, and using incorrect units. It is important to carefully label angles and sides and double-check calculations to avoid these errors.

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