Trigonometry

The page about Trig, the most beloved subjected taught in PreCal. Hehe, you may not like, but you'll use it a lot in Calc, so suck it up and learn it.

Today, we learned about Polar Form (or Trig Form) of complex numbers. Here's just the basic outline for a refresher.

**The angle Theta will be called x in this lesson.

If z = a + bi, then:

r = sqrt(a^2 + b^2)        a = r*cosx       b = r*sinx

z = r*(cosx + i*sinx)

So, we have our mulitply/divide/power functions:

z1z2 = r1r2[cos(x1+x2) + i*sin(x1+x2)]

z1/z2 = r1/r2[cos(x1-x2) + i*sin(x1-x2)]

z^n = r^n [cos(nx) + i*sin(nx)]

In Rectangular coordinates, instead of a and b, we use x and y, so remember:

x = rcos(theta)        y = rsin(theta)

r = +- sqrt(x^2 + y^2)

and theta = arctan(y/x)

So, we've moved onto Conic Sections:

the basic: Given a line l,

tan(theta) = m ; where theta=the angle from positive x-axis to the line and m is the slope of the line.

I hope this helps some people out!