Thread: trig identity problem (sort of)

If tanΘ is undefined and 9pi ≤Θ ≤ 10.265pi ,find sinΘ

i have tried to solve this and came up with the answer of sinΘ = -1 but this is an incorrect answer according to the answers section in the back of my text book...

i honestly can't see were i've made a mistake

please and thank you for your help!

If the tangent is undefined, what does that say about the angle $\displaystyle \theta$? And if you have a restriction on where $\displaystyle \theta$ can be, that should uniquely define the problem.

I can't either. tan θ is undefined if θ is an odd multiple of pi/2. If tan θ is undefined and 9 pi < θ < 10.265pi, then $\displaystyle \theta = \frac{19\pi}{2}$, and so $\displaystyle \sin \frac{19\pi}{2} = \sin \frac{3\pi}{2} = -1$. Is this the complete problem?

i know i still can't find where i made a mistake!

this is how i approached the problem:

tan Θ = sin Θ / cos Θ
and tan Θ can only be undefined if cos Θ = 0

well, cos Θ = 0 if Θ = 1/2pi + 2npi or 3/2pi + 2npi

then i found where 9 pi < θ < 10.265 pi which was at θ= 19pi/2

and i used my calculator to solve sin (19pi/2) to get and answer of -1

this is the complete problem...

and thank you to all who helped me!

a special thanks to eumyang because i never made the connection that tan θ is undefined at odd multiple of pi/2