Question

If `sinx=5/6`, find `cosx`?

Answer 1

`cosx=+-sqrt11/6`

Explanation:

As `sinx=5/6` and `sin^2x+cos^2x=1`

we have `cosx=sqrt(1-sin^2x)=sqrt(1-(5/6)^2)`

= `sqrt(1-25/36)=sqrt(11/36)=+-sqrt11/6`

Note that sign of `cosx` colud be + or -, depending on the quadrant in which `x` lies. As `sinx` is positive, `x` lies in `Q1` or `Q2`.

If `x` is in `Q1`, `cosx=sqrt11/6` and if `x` lies in `Q2` `cosx=-sqrt11/6`.