For a uniformly random real number \(k\) in the interval \([-10, 0],\) the probability that \(\sin^4 \theta - \sin^2 \theta - k = 0\) has at least one real solution \(\theta\) can be expressed as \(\dfrac{a}{b}\) for positive coprime integers \(a\) and \(b.\) What is the value of \(a+b\)?

This problem is posed by Michael T.

×

Problem Loading...

Note Loading...

Set Loading...