Question

Express the following as a function of its correlated acute angle and evaluate.
tan(39pi/4)

Answer 1

sammeeeyyyy, what's up? stuck on this?

Answer 2

So you have 39 of these pi/4's ?
That's too many, gotta unwind that angle.

Answer 3

let's spin backwards one full rotation by subtracting 2pi,\[\Large\rm \frac{39\pi}{4}-2\pi=\frac{39\pi}{4}-\frac{8\pi}{4}=\frac{31\pi}{4}\]Mmm that's no good, we gotta spin back a few more times, ya?

Answer 4

I got 7pi/4, after unwind it again and again... @zepdrix

Answer 5

Ah yes that looks right

Answer 6

What should I do next?

Answer 7

\[\Large\rm \tan\left(\frac{7\pi}{4}\right)\]AHHH I dunno, this is just unit circle stuff...
lot of memorization...

Answer 8

All of the pi/4's give us a 1 or a -1 when we take the tangent of them.

Answer 9

We're in which quadrant with our angle?

Answer 10

Quadrant 4?

Answer 11

Mmm k good.
If you can't seem to get the sign right, you can relate tangent back to sine and cosine.
\[\Large\rm \tan=\frac{\sin}{\cos}\]What's the sign going to be in quadrant 4? we getting a 1 or a -1?

Answer 12

-1

Answer 13

yay good job \c:/