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

1 Answer
Nghi N
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

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