Question

Can someone please help me in this question?

Find (exactly) all solutions in [0, 2pie] for each equation:

tan(t) = 1/tan(t)

Answer 1

Use \[ \tan(t) =\frac{\sin(t)}{\cos(t)} \]

Answer 2

Plug that into your equation, what do you get?

Answer 3

Hint: There are exactly two solutions in the interval [0, 2Pi].

Answer 4

Oh okay, so would I plug the 0,2Pi in t?

Answer 5

? You don't

Answer 6

hmm the answer is -.4995 but they don't seem to give me any reference like a graph or something :S

Answer 7

lol the answer can impossibly be negative because the problem constraint is that t is in [0,2Pi]

Answer 8

The answers are Pi/4 and 5Pi/4

Answer 9

lol thats wierd, i'll look over it again, thanks for the help tho I appreciate it.

Answer 10

You need to look for values t such that \[ \sin^2(t) = \cos^2(t) \]

Answer 11

Alternatively, note that tan x = 1/tan x if and only if tan^2 x = 1, hence
\[\tan x = \pm 1\]
Look now at the graph of tan x on the interval [0, 2 pi] ...

Answer 12

oh ic, thx