Suppose $\theta$ is in the interval $\left(90^{\circ}, 180^{\circ}\right)$. Find the sign of the following. \[ \sin \left(\theta-90^{\circ}\right) \] Choose whether the sign of $\sin \left(\theta-90^{\circ}\right)$ is positive or negative. Negative Positive

Step 1 ：Suppose \(\theta\) is in the interval \(\left(90^{\circ}, 180^{\circ}\right)\). We need to find the sign of the following: \[\sin \left(\theta-90^{\circ}\right)\]

Step 2 ：The sine function is positive in the first and second quadrants, and negative in the third and fourth quadrants.

Step 3 ：Since \(\theta\) is in the interval \(\left(90^{\circ}, 180^{\circ}\right)\), \(\theta-90^{\circ}\) will be in the interval \(\left(0^{\circ}, 90^{\circ}\right)\), which is in the first quadrant.

Step 4 ：Therefore, \(\sin \left(\theta-90^{\circ}\right)\) should be positive.

Step 5 ：Final Answer: The sign of \(\sin \left(\theta-90^{\circ}\right)\) is \(\boxed{Positive}\).