# Thread: I need help understanding this example in my book.

1. ## I need help understanding this example in my book.

If A falls on Quadrant II and B falls in Quadrant III, then what the sign of cos(A+B).

its is greater than 0 or less than 0.

and then another example just like the same.

If A falls on Quadrant II, and B falls on Quadrant III, then what is the sign of sin(A-B)
it's is greater than 0 or less than 0.

2. ## Re: I need help understanding this example in my book.

Hello, TrimHonduras!

$\displaystyle \text{If }A\text{ is in Quadrant II and }B\text{ is in Quadrant III,}$
. . $\displaystyle \text{what is the sign of }\cos(A+B)\,?$

$\displaystyle \begin{array}{cccccccccc}A \in \text{Q II} & 90^o &<& A &<& 180^o \\ B \in \text{Q\,\!III} & 180^o &<& B &<& 270^o \\ \text{Add:} & 270^o &<& A+B &<& 450^o \end{array}$

Hence, $\displaystyle A+B$ is in Quadrant I or IV.

Therefore:-$\displaystyle \cos(A+B)$ is positive.

$\displaystyle \text{If }A\text{ is in Quadrant II and }B\text{ is in Quadrant III,}$
. . $\displaystyle \text{what is the sign of }\sin(A-B)\,?$

We have:-$\displaystyle \begin{Bmatrix}90^o &<& A &<& 180^o \\ 180^o &<& B &<& 270^o \end{Bmatrix}$

The minimum difference is when $\displaystyle A = 180^o$ and $\displaystyle B = 180^o.$
. . Hence: .$\displaystyle A-B \:=\:0^o$

The maximum difference is when $\displaystyle A = 90^o$ and $\displaystyle B = 270^o.$
. . Hence:-$\displaystyle A-B \:=\:-180^o$

Then:-$\displaystyle -180^o \:<\:A-B \:<\:0^o$

Hence, $\displaystyle A-B$ is in Quadrant III or IV.

Therefore:-$\displaystyle \sin(A-B)$ is negative.

3. ## Re: I need help understanding this example in my book.

thank you so much... Now I understand