# Thread: another problem ><

1. ## another problem ><

im good at nearly all maths topics but god i fail at trigonometry so much lol anywho...

find all possible solutions for θ within the range 0 < θ < 2Pi that satisfy

tanθ = tanα

where α > 0

i dont even know how to go about starting this let alone answering it ^^
so can anyone talk me through this? muchly appreciated and mega-thanks in advance

2. Originally Posted by Phoenixium
im good at nearly all maths topics but god i fail at trigonometry so much lol anywho...

find all possible solutions for θ within the range 0 < θ < 2Pi that satisfy

tanθ = tanα

where α > 0

i dont even know how to go about starting this let alone answering it ^^
so can anyone talk me through this? muchly appreciated and mega-thanks in advance
Since $\alpha$ is just a constant, you can think of this as trying to find where the graph of $tan(/theta)$ intersects the line $y = tan(\alpha)$. Glancing at the graph below, which has a sample line running through it, you can see that the function $y = tan(\theta)$ has a period of $\pi$. Thus you will have two possible solutions in the given range.

So the possible values of $\theta$ are
$\theta = \alpha + n \pi$ where n = 0, 1

-Dan

3. thanks that helped so much ^^