2. ## ONE easy trig question

Don't mind the Alvira bit. Please explain algebraically how the diagram is in this equation: d km= 3tan((pi)x)

3. Originally Posted by delicate_tears
Don't mind the Alvira bit. Please explain algebraically how the diagram is in this equation: d km= 3tan((pi)x)
note that on a right triangle, we have $\displaystyle \tan\theta=\frac{b}{a}$ where $\displaystyle b$ is the opposite side and $\displaystyle a$ is the adjacent side.

thus, from your figure, we have $\displaystyle \tan\theta=\frac{d}{3} \Rightarrow d = 3\tan\theta$..

now, how come that $\displaystyle \theta = \pi t$?

it was said that light spans a complete rotation (1 rev = $\displaystyle 2\pi$) every two minutes and thus the rate of revolution is $\displaystyle \pi$ per minute.

so, at time t minutes, the light spans $\displaystyle \pi$ times that time $\displaystyle t$, and that is the angle of rotation, thus we have $\displaystyle d = 3\tan(\pi t)$

aww, you were using $\displaystyle x$.. well it is just the same.. they are just dummy variables.

4. and to answer the second part, note that tangent is not defined on $\displaystyle \frac{\pi}{2} + n\pi$..

5. Originally Posted by mr fantastic
Said where? Certainly not in this thread. Is this a continuation of a question discussed in another thread?
yeah, actually..