Posted by girly93 on Monday, February 9, 2009 at 2:55am.
i don't understand the sine and cosine rules.
1/2 ab sinC
and cosA= b2 + c2 - a2
what???
i have asked my teacher but i still don't get it.
Your question makes no sense to me.
The law of cosines is this
a^2=b^2+c^2 - 2bc * CosA
I have no idea what 1/2 ab SinC is , unless it is the area formula for a triangle. You need to be more specific.
The law of cosines, in one form, is
a^2 = b^2 + c^2 - 2bc cos A
The law of sines is
a/sin A = b/sinB = c/sinC
= 2R
Your cosA equation is incorrect.
(1/2) a b sin C is a formula for the area of a triangle, and has nothing to do with the law of sines.
For more about these equations, see
http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/web-sinecostri.pdf
The sine and cosine rules are mathematical formulas commonly used in trigonometry to calculate the lengths of sides or measurements of angles in triangles.
Let's break them down:
1. The sine rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be written as:
a/sinA = b/sinB = c/sinC
In this formula, 'a', 'b', and 'c' are the lengths of the sides of the triangle, and 'A', 'B', and 'C' are the measures of the angles opposite these sides. The sine rule helps you find the missing side lengths or angles of a triangle when you know the lengths of some sides and the measures of some angles.
The formula you mentioned, 1/2 * ab * sinC, is actually the formula to calculate the area of a triangle using the lengths of two sides and the included angle. It's derived from the sine rule. The area of a triangle is half the product of two sides and the sin of the included angle.
2. The cosine rule is used to calculate the length of one side or the measure of an angle in a triangle when you know the lengths of the other two sides. It can be written in three different forms, depending on what you want to find:
a^2 = b^2 + c^2 - 2bc * cosA
b^2 = a^2 + c^2 - 2ac * cosB
c^2 = a^2 + b^2 - 2ab * cosC
In these formulas, 'a', 'b', and 'c' are the lengths of the sides of the triangle, and 'A', 'B', and 'C' are the measures of the angles opposite these sides. The cosine rule allows you to find missing side lengths or angles in a triangle when you know the lengths of two sides and the included angle.
To better understand these rules, it may be helpful to practice solving sample problems or using geometric diagrams. Additionally, discussing the concept further with your teacher or seeking additional resources might provide more clarity.