How do you find the exact value of #3tantheta=cottheta# in the interval #0<=theta<360#?

Question

2758 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-04T08:24:42

The answer is #theta={30º,150º,210º,330º} #

We use,

#tantheta=sintheta/costheta#

#cottheta=costheta/sintheta#

and #sin^2theta+cos^2theta=1#

and #0<=theta<=360#

Our equation is,

#3tantheta=cottheta#

#3sintheta/costheta=costheta/sintheta#

#3sin^2theta=cos^2theta#

#3sin^2theta=1-sin^2theta#

#4sin^2theta=1#

#sintheta=+-1/2#

#theta=30º, 150º, 210º, 330º#