# Math Help - Solving trig Equations

1. ## Solving trig Equations

I need help on these questions...i really dont get them:

solve:
cosx (cosx-1)=0

and these next two are on the inerval of [0, 2pi)

2sin^2x = 2+cosx

secx + tanx=1

and theres one on harmonic motion i dont get:

the position of the weight relative to the point of equilibrium is given by:
y= 1/12 (cos8t-3sin8t)
find the times when the weight is at the point of equilibrium (y=0) for 0 is less than/ equal to t that is less than/equal to 1.

Thanks!

2. Originally Posted by >_<SHY_GUY>_<
I need help on these questions...i really dont get them:

solve:
cosx (cosx-1)=0

$\cos{x}(\cos{x-1})=0$

Set each of the factors equal to zero because anything times zero, equals zero..right?

$\cos{x}=0$

We know that cosx=0 for $\frac{\pi}{2}$ and $\frac{3\pi}{2}$. Generalizing that to include their multiples we have:

$x=\frac{\pi}{2}\pm\pi k$

Now try it with the other factor:

$\cos{x}-1=0$

Add one to each side, then think about the unit circle to determine for what values cosx=1. Remember, on this one you want to solve for all values, not just from 0 to $2\pi$.