# Solving a trig equation?

• Oct 26th 2009, 11:59 AM
nascar77
Solving a trig equation?
I need to solve the following trig expression:

4cos4θ=0 (reads four cosine four theta)

Its the formula of a graph but i need to find the zeros or the points that it passes through the pole (its a polar graph)

Would i use the double angle formula or find when cos=0 and multiply the period by 4? Im confused(Worried)
• Oct 26th 2009, 01:35 PM
mathgirlie
I think you are making this more difficult than it really is....

4cos4θ=0

the four is insignificant (because 0/4 is still 0). so now we have:

cos4θ=0.

I think the 4 is confusing you so let x=4θ so now we have:

cosx=0
and the solutions to that is when x=pi/2 or 3pi/2

now substitute 4θ in for x and you have
4θ=pi/2 and 4θ=3pi/2
so dividing by four yields:
θ=pi/8 and θ=3pi/8

Hope that helped!!
• Oct 26th 2009, 01:51 PM
pickslides
Also what domain are you looking for solutions in?

The previous post gives the solutions on $x \in \left[0,\frac{\pi}{2}\right]$

You can find all solutions as $x = \frac{(2n+1)\pi}{8}, n\in \mathbb{Z}$