Question

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

Answer 1

`+- 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