Question

tan x = -k
Find tan (0.5 pi +x) given that x is obtuse

Answer 1

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Answer 2

why not just try the addition formula?

Answer 3

That will give infinity in denominator

Answer 4

welp, didn't think of that.\[\tan(\pi/2 + x) = -\cot x\]

Answer 5

Yeah but that requires me to prove that identity and the question doesnt ask to do it

Answer 6

The method basically revolves around using the 4 quadrants and trying to figure out the result

Answer 7

\[\frac{\tan \pi/2 + \tan x}{1-\tan \pi/2 \tan x}\]\[= \frac{1+\frac{\tan x}{\tan \pi/2}}{\frac{1}{\tan \pi/2} - \tan x}\]But \(1/\tan \pi/2 =\cot\pi/2 = 0\).

Answer 8

I know the identity but the question prohibits me to use it

Answer 9

Its like doing this

Answer 10

Yeah, that's how I think about trig. :P

Answer 11

Since the tan (p/b) will give k and the quadrant is second so the answer is -k

Answer 12

but I dont know how to use the same technique for an obtuse triangle

Answer 13

angle*

Answer 14

well, you only need to know how to find the sines and cosines really

Answer 15

and how would I do that(on a similar note: If I can figure out the sines and cosines they would require the same technique to figure out the tan. So shouldn't I just focus on tan)

Answer 16

yeah, but there's no nice way to see tan on a unit circle. ok maybe you can.

Answer 17

Any idea how to do that?

Answer 18

I don't know. Can you show that \(\sin (\pi/2 + x) = -\cos x\) for an obtuse angle? (Actually any angle.)

Answer 19

Actually we haven't been taught the addition formula (although I know it) so I cant use it

Answer 20

Ugh, typo. I meant \(\sin (\pi/2 + x) = \cos x\). And no, without the addition formula.

Answer 21

Can you think of some way to utilise the quadrant technique this is so far I have gotten