POLAR COORDINates --TRIG HELPS ?

Question

Im graphing r^2=cos(2u)

and I'm trying so solve

cos(2u) >=0

so I let w b x =2u

cosx >=0 ...now the book says +-Pi/4 +-3Pi/4

but I want to do it from the CAST diagram not from the identitity cos(-x)=cosx ....

If I trace it around I only see how I get Pi/2 to 3Pi/2 =x

and therefore Pi/4 and 3Pi/4 is the interval ....but how do I get the negative ones ...

I tried tracing from -Pi to Pi but couldnt do it either ....

Helps

Answer 1

cos x > = 0 means that x is in the first and fourth quadrants or

-pi/2 < x < pi/2 or 3pi/2 < x < 5pi/2

(Your idea of pi/2 to 3pi/2 would be the second and third quadrants.)

-pi/2 < 2u < pi/2 or 3pi/2 < 2u < 5pi/2

-pi/4 < u < pi/4 or 3pi/4 < u < 5pi/4 (= -3pi/4)

The book's answer u = +/- pi/4 or +/- 3pi/4 seems to be the answer to cos 2u = 0.