Expert: Paul Klarreich - 8/1/2009

Question
Solve Cos 2A = 0 on the interval o less than or equal to A i sless than or equal to 2pi

MY work;

cos(2A) = 0
0 at pi/2 and 3pi/2
(2A) = pi/2 + 2kpi or (2A)= 3pi/2 + 2kpi

simplify :
         A= pi/4 + kpi or (A) = 3pi/4+kpi
Now i plugged in values from -1 to and 2 into both the equation and got this:

For -1 ; -3pi/4, -pi/4.
for 0;   pi/4, 3pi/4
for 1;   5pi/4, 7pi/4
for 2;  9pi/4, 11pi/4

My question: According to the interval i have to use values only between 0 and 2pi. From the values i got which ones can i use ??

Answer
Questioner: Raj
Country: United States
Category: Advanced Math
Private: No
Subject: Exact Value (Precalc)
Question: Solve Cos 2A = 0 on  0 <= A <= 2pi

>> You mean  0 <= A < 2pi, not <= 2pi,  because  0,2pi are coterminal.  We don't include both of them

MY work;

cos(2A) = 0
0 at pi/2 and 3pi/2       << Good.

(2A) = pi/2 + 2kpi or (2A)= 3pi/2 + 2kpi

simplify :
        A = pi/4 + kpi or (A) = 3pi/4+kpi

Now i plugged in values from -1 to and 2 into both the equation and got this:

For -1 ; -3pi/4, -pi/4.   << No good.
for 0;   pi/4, 3pi/4   << Yes.
for 1;   5pi/4, 7pi/4  << Yes.
for 2;  9pi/4, 11pi/4  << No good.

My question: According to the interval i have to use values only between 0 and 2pi. From the values i got which ones can i use ??