trig equation cot theta = 1: how to find theta?

[kpx001]

how would i find the exact values of the trig functions if theta is an acute angle for which cot theta = 1 ?

sin(x)/cos(x) = 1

sin(x) = cos(x)

from there i dunno what to do

 

[skeeter]

\(\displaystyle \L \cot{\theta} = 1\)

\(\displaystyle \L \frac{\cos{\theta}}{\sin{\theta}} = 1\)

\(\displaystyle \L \cos{\theta} = \sin{\theta}\)

know your unit circle for quadrant I?
\(\displaystyle \L \cos{\theta} = \sin{\theta}\) at \(\displaystyle \L \theta = \frac{\pi}{4}\)

 

[kpx001]

sqroot(2)/2 = sqroot(2)/2 ???
i dunno what the final answer is though

 

[kpx001]

woops

-sqroot(2)/2 = sqroot(2)/2

 

[skeeter]

you really need to learn this, backwards/forwards/upside-down/inside-out ...

 

[kpx001]

once i get sqroot(2)/2 = sqroot(2)/2
what do i do next?

 

[skeeter]

how about answering the original question ?

how would i find the exact values of the trig functions if theta is an acute angle for which cot theta = 1 ?

using the equation, and our knowledge of the unit circle, it was determined that the acute angle in question equaled pi/4 ...

cos(pi/4) = sin(pi/4) = sqrt(2)/2

tan(pi/4) = cot(pi/4) = 1

sec(pi/4) = csc(pi/4) = sqrt(2)

you're done.