Using the Unit Circle., find the exact value of this trig function: backslash (backslash sin(270^wedge backslash circ) ( ). -1 undefined

To find the exact value of $\sin(270^\circ)$ using the unit circle, we need to understand the position of the angle $270^\circ$ on the unit circle.<br /><br />The unit circle is a circle with a radius of 1, and it is used to define the trigonometric functions sine, cosine, and tangent. The angle $270^\circ$ is located in the third quadrant of the unit circle.<br /><br />In the unit circle, the sine of an angle is defined as the y-coordinate of the point where the terminal side of the angle intersects the unit circle.<br /><br />For the angle $270^\circ$, the terminal side intersects the unit circle at the point $(0, -1)$. Therefore, the sine of $270^\circ$ is equal to the y-coordinate of this point, which is $-1$.<br /><br />So, the exact value of $\sin(270^\circ)$ is $-1$.