Determine the signs of the six trigonometric functions of an angle in standard position with the given measure. $875^{\circ}$ Determine if the value of $\sin 875^{\circ}$ is positive or negative. Positive Negative Is the value of $\cos 875^{\circ}$ positive or negative? Negative Positive What is the sign of the value of $\tan 875^{\circ}$ ? Negative Positive Is the sign of the value of $\csc 875^{\circ}$ positive or negative? Negative Positive Determine if the value of $\sec 875^{\circ}$ is positive or negative. Negative Positive

Step 1 ：Convert the angle from degrees to radians. The angle in radians is approximately \(15.27\).

Step 2 ：Calculate the values of the six trigonometric functions using the numpy library's trigonometric functions. The values are approximately: \(\sin 875^{\circ} = 0.42\), \(\cos 875^{\circ} = -0.91\), \(\tan 875^{\circ} = -0.47\), \(\csc 875^{\circ} = 2.37\), \(\sec 875^{\circ} = -1.10\), and \(\cot 875^{\circ} = -2.14\).

Step 3 ：Determine the sign of these values. The signs are: \(\sin 875^{\circ}\) is positive, \(\cos 875^{\circ}\) is negative, \(\tan 875^{\circ}\) is negative, \(\csc 875^{\circ}\) is positive, \(\sec 875^{\circ}\) is negative, and \(\cot 875^{\circ}\) is negative.

Step 4 ：Final Answer: The signs of the six trigonometric functions of an angle in standard position with the given measure $875^{\circ}$ are: \(\sin 875^{\circ}\) is \(\boxed{Positive}\), \(\cos 875^{\circ}\) is \(\boxed{Negative}\), \(\tan 875^{\circ}\) is \(\boxed{Negative}\), \(\csc 875^{\circ}\) is \(\boxed{Positive}\), \(\sec 875^{\circ}\) is \(\boxed{Negative}\), and \(\cot 875^{\circ}\) is \(\boxed{Negative}\).