How do you use #sintheta=1/3# to find #tantheta#?

1 Answer
Jan 8, 2017

#+- sqrt2/4#

Explanation:

First find cos t.
#cos^2 t = 1 - sin^2 t#
#cos ^2 t = 1 - 1/9 = 8/9#
#cos t = +- (2sqrt2)/3#
#tan t = sin t/(cos t) = +- (1/3)(3/(2sqrt2)) = +- 1/(2sqrt2) = +- sqrt2/4#
Note about the signs of tan t.
On the unit circle:
sin t = 1/3 --> cos t either + or - , there for --> tan t either + or -
Check by calculator.
#sin t = 1/3# --> #t = 19^@47# and #t = 180 - 19.47 = 160^@53#
tan 19.47 = 0.35 and tan 160.53 = - 0.35
#+- sqrt2/4 = +- 1.414/5 = +- 0.35# OK