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.

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