Chapter 6.2, Problem 1E

To determine

To find: The complete sentence for the given cosine function.

Answer to Problem 1E

Thestandard form for $\cos C=\frac{a^2+b^2-c^2}{2ab}$ is $c^2=a^2+b^2-2ab\cos C$ .

Explanation of Solution

Given:

The given equation is $\cos C=\frac{a^2+b^2-c^2}{2ab}$ .

Calculation:

Consider the sides of the triangles are $a,b$ and c. Where, c is the longest side.

Then, the square of the third side of the triangle is,

  $\begin{array}{l}{c}^2=a^2+b^2-2ab\cos C\\ \cos C=\frac{a^2+b^2-c^2}{2ab}\end{array}$

Thus, the standard form is $c^2=a^2+b^2-2ab\cos C$ .