Posted by **Katy** on Monday, April 23, 2012 at 12:40pm.

how do u find period, all angles and name 8 angles for these????????

1)cosxcos2x+sinxsin2x=sqrt(2)/2

2)5cosxsinx+2cosx=0

- pre-calculus help:(((((((( -
**Reiny**, Monday, April 23, 2012 at 12:56pm
You have to know your expansion formulas

to recognize that

cosx cos2x + sinx sin2x = cos(x-2x)

= cos(-x)

but cos(-x) = cos(x)

so,

cosx = √2/2

x = 45° or 315°

in radians: x = π/4 or 7π/4

since the original = cosx, and the period of cosx = 360°, the period of the original is 360°

so add/subtract 360° to any answer to yield more answers until you have 8 of them

e.g. 45+360 = 405 , another answer

5cosxsinx + 2cosx=0

cosx(5sinx + 2) = 0

cosx = 0 or sinx = -2/5

if cosx =0, then x = 90° or 270°

if cosx = -2/5, x = appr. 113.6° or 246.4°

period again is 360° , etc

(it asked for all angles, no such thing there would be an infinite number of angles as solutions)

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