Chapter 3, Problem 12Q

The x and y components of four vectors $\stackrel{\to }{a}\text{, }\stackrel{\to }{b}\text{, }\stackrel{\to }{c}$ and $\stackrel{\to }{d}$ are given below. For which vectors will your calculator give you the correct angle 8 when you use it to find θ with Eq. 3-6? Answer first by examining Fig. 3-12, and then check your answers with your calculator.

$\begin{array}{l}{a}_x=3a_y=3 c_x=-3c_y=-3\hfill \\ b_x=-\text{3}{b}_y=3 d_x=3 d_y=-3\hfill \end{array}$

$a=\sqrt{a_x^2+a_y^2}\text{ and tan }\theta =\frac{a_y}{a_x}\text{(3-6)}$

Figure 3-12 Three useful curves to remember. A calculator's range of operation for taking inverse trig functions is indicated by the darker portions of the colored curves.