Posted by Ann on Friday, May 10, 2013 at 11:50am.
What is the exact answer to cos^2x  sin^2x = 0 for between 0 and 2pi?
I got x = pi/4 and x = 5pi/4. But the answer key says there are two additional answers which are 3pi/4 and 7pi/4. I don't know how to get these. Any help is much appreciated!

Math  Reiny, Friday, May 10, 2013 at 1:04pm
cos^2x  sin^2x = 0
cos (2x) = 0
2x = π/2 or 2x = 3π/2
x = π/4 or π = 3π/4
but the period of cos (2x) is π
so by adding π to any answer will yield a new answer
new answers :
π/4+π = 5π/4
3π/4 + π = 7π/4
Since I converted to cos 2x, there would be 2 complete cosine curves for 0 to 2π
other way:
cos^2 x = sin^2 x
sin^2 x/cos^2 x = 1
tan ^2 x = 1
tan x = ± 1
x = 45°, 135° , 225° , 315°
or
π/4 , 3π/4 , 5π/4 , 7π/4

Math  Ann, Friday, May 10, 2013 at 8:28pm
Thanks!

Math  Anonymous, Wednesday, May 22, 2013 at 8:23am
There is an expression some people use that says, “What you put into it is what you get out of it.” People might use this expression to describe your skills at a sport or activity and how that relates to the amount of time and effort you spend practicing that activity. Does this expression apply to functions? How?

Math  Bob, Tuesday, May 6, 2014 at 9:44am
There is an expression some people use that says, “What you put into it is what you get out of it.” People might use this expression to describe your skills at a sport or activity and how that relates to the amount of time and effort you spend practicing that activity. Does this expression apply to functions? How? Give an example to support your answer.

dsadsasdjkasldkjaslkdjl  mansdasjdaksjndkjasndjsadk, Wednesday, May 14, 2014 at 4:52pm
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