Question

Make cos the c the subject of the formula c^2=a^2+b^2-2ab cos C

Answer 1

To find 'cos C' from the formula c² = a² + b² - 2ab cos C, subtract a² + b² from both sides, divide by -2ab, and rearrange to make cos C the subject.

Step-by-step explanation:

The student is asking to make ‘cos C’ the subject of the formula c² = a² + b² - 2ab cos C, which is an application of the Law of Cosines. To isolate ‘cos C’, we must rearrange the equation:

First, subtract a² + b² from both sides of the equation, which gives c² - a² - b² = -2ab cos C.

Next, divide both sides of the equation by -2ab, resulting in (c² - a² - b²) / -2ab = cos C.

Finally, rearrange it to cos C = (a² + b² - c²) / 2ab.

Through these steps, we express cos C as the subject of the formula.