Trigo Cosine Rule
When applying the Cosine Rule, there are two forms you can use, depending on whether you are finding an unknown side or an unknown angle. When solving for an unknown angle, you will learn how to rearrange and derive the formula from the original Cosine Rule expression.
Related Lessons:
Cosine Rule - Find Unknown Side
The Cosine Rule formula is \(a^2=b^2+c^2-2bc\ cos{A}\). The Cosine Rule follows a clear pattern that helps you remember how the sides and angle are related.:
- \(a^2\) is opposite \(cos{A}\)
- The sign after \(b^2\) and \(c^2\) is always a negative
Cosine Rule - Find Unknown Angle
To find the unknown angle using Cosine Rule, students are encouraged to rearrange and derive the formula from the original Cosine Rule expression.
\[
\begin{align*}
a^2&=b^2+c^2-2bc\ cos{A}\\
2bc\ cos{A}&=b^2+c^2-a^2\\
\ cos{A}&=\frac{b^2+c^2-a^2}{2bc}
\end{align*}
\]
Example 1
In this first example, we are asked to find the length of side AB.
Example 2
In this second example, we are asked to find the unknown angle ABC.