If tan theta equal - square root of 22 divided by 11 and pie/2 is less than theta and theta is less than pies, what is the cos of theta in simplified rationalized form

2 answers

Negative square root of 22*
Grrrr! pi, not pie!!! Pie is what you eat.

Other than that, why not use real math symbols, instead of all those messy words??

tan θ = -√22/11 and π/2 < π < π

Draw the triangle in standard position.

tanθ = y/x = √22/-11
sinθ = y/r
cosθ = x/r

You will see that
y = √22
x = -11
r = √143

Now you can easily evaluate cosθ and sinθ