How Do You Calculate the Length of Vector C Using Components and Trigonometry?

[sami23]

Homework Statement

Find the length of the vector C starting from the components given in Equations 3 and 4.
Express C in terms of A, B, and theta.

Homework Equations

3. C_x= A + Bcos(\theta),
4. C_y = Bsin(\theta).

The Attempt at a Solution

C = \sqrt{C_x ^2+C_y ^2}
C = \sqrt{A^2+(Bcos\theta)^2+(Bsin\theta)^2}
using trig identity cos² \theta+sin² \theta=1
C = \sqrt{A^2+2B^2} ?

 

[CompuChip]

You have all the right ingredients, but be careful!

(A + B \cos\theta)^2 is not the same as A^2 + (B \cos\theta)^2.

This is a classical trap... (x + 1)² is not equal to x² + 1²... to see what it does equal, you can write it out as (x + 1)(x + 1) and expand the brackets.

 

[sami23]

C = \sqrt{A^2 + 2ABcos\theta + B^2}

 

[CompuChip]

Now you're just sloppy and maybe guessing a bit, aren't you? :)
Please work it out carefully and you'll get the right answer.