Determine the values of theta, 0=theta=2pi, for which tan theta = -sqrt (sec^2 theta - 1)

Question

Should I use a graphing calculator for this? 

Answer 1

Hi -- 

 

I think this question makes no sense:

 

sec theta = 1/cos theta therefore

 

tan theta = - sqrt( (1/cos theta )^2-1)

tan theta = - sqrt(( 1^2/cos^2 theta)-1)

tan theta = - sqrt((1 - cos^2 theta)/cos^2 theta)

but sin^2 theta= 1 - cos^2 theta

therefore 

tan theta = - sqrt(sin^2 theta / cos^2 theta)

tan theta = -sqrt( (sin theta/cos theta)^2)

but 

tan theta= sin theta/cos theta

therefore 

tan theta = - sqrt(tan^2 theta)

and 

tan theta = - tan theta ?????

 

There is no theta that satisfies the above equation.