1. The problem asks which trigonometric identity is NOT correct for a point $(x,y)$ on the unit circle with rotation angle $\theta$. 2. Recall the unit circle definitions: - $\cos(\theta) = x$ (the x-coordinate) - $\sin(\theta) = y$ (the y-coordinate) - $\sin(-\theta) = -\sin(\theta)$ (sine is an odd function) - $\cos(-\theta) = \cos(\theta)$ (cosine is an even function) 3. Given these, check each statement: - $\cos(\theta) = x$ is correct. - $\sin(-\theta) = $ (incomplete in question, but should be $-\sin(\theta)$). - $\sin(\theta) = y$ is correct. - $\cos(-\theta) = x$ is incorrect because $\cos(-\theta) = \cos(\theta)$, so it equals $x$, but the question implies a mismatch or incomplete expression. 4. The incorrect statement is the one involving $\sin(-\theta)$ if it is not equal to $-\sin(\theta)$ or the incomplete expression. 5. For Question 20, find the reference angle for $-310^\circ$: - Add $360^\circ$ to get a positive coterminal angle: $-310^\circ + 360^\circ = 50^\circ$ - The reference angle is $50^\circ$. Final answers: - Question 19: The incorrect identity is $\sin(-\theta) = $ (if incomplete or not equal to $-\sin(\theta)$). - Question 20: Reference angle is $50^\circ$.