ACTIVITY 3.9
OBTAINING MODULE AND ARGUMENT FROM COMPONENTS

Knowing the components of vector = (v₁, v₂), we can calculate easily his module ||: . To calculate his argument , we take in account that tan = and by the moment  we can write = Arctan.

Now the Arctan(x) function, that in the calculators correspond to the button tan ^-1 generally, return an angle comprised between -90 º and 90 that it has by tangent x. Then, if the vector is in the 2nd or 3rd quadrant we must effect a correction to Arctan  value consistent in adding 180 º.

Summarizing, the argument of a vector = (v₁, v₂)  it calculates:
                                         
If= (v₁ , v₂) is in the 4rth quadrant, the calculation of Arctan  gives negative; we can become it in positive adding 360 º.

INTERACTIVE ACTIVITY

You calculate the modules and arguments of the next vector and express them in the M _a form. Later you use the applet of the right side to draw them and check the results.

= (3,4)	= (-6,4)
= (-8,-6)	= (3,-5)
= (5,0)	= (0,4)
= (-7,0)	= (0,-6)

SOLUTION

END OF ACTIVITY 3.9
OBTAINING MODULE AND ARGUMENT FROM COMPONENTS