Question

If `costheta=-4/7`, what are the values of `sin theta` and `tan theta`?

Answer 1

`sin t = +- sqrt33/7`
`tan t = +- sqrt33/4`

Explanation:

Use trig identity:
`sin^2 t = 1 - cos^2 t`
In this case:
`sin^2 t = 1 - 16/49 = 33/49` --> `sin t = +- sqrt33/7`
t could be either in Quadrant II and Quadrant III (cos t negative), there for both values could be answers.
The same for tan t where both answers are acceptable.
`tan t = sin/(cos) = +-(sqrt33)/7(- 7/4) = +- (sqrt33)/4`