Sketch an angle $\theta$ in standard position such that $\theta$ has the least possible positive measure, and the point $(\sqrt{10}, \sqrt{6})$ is on the terminal side of $\theta$. Find the values of the six trigonometric functions for the angle. Do not use a calculator. Sketch an angle $\theta$ in standard position such that $\theta$ has the least possible positive measure, and the point $(\sqrt{10}, \sqrt{6})$ is on the terminal side of $\theta$. Choose the correct graph below. A. B. c. D.

Step 1 ：Sketch an angle \(\theta\) in standard position such that \(\theta\) has the least possible positive measure, and the point \((\sqrt{10}, \sqrt{6})\) is on the terminal side of \(\theta\).

Step 2 ：The standard position of an angle is when its vertex is at the origin and one ray is on the positive x-axis. The terminal side of the angle is the ray that rotates from the initial side.

Step 3 ：The six trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent. These can be calculated using the coordinates of the point on the terminal side.

Step 4 ：The x-coordinate corresponds to the adjacent side of the right triangle formed by the angle, the y-coordinate corresponds to the opposite side, and the hypotenuse is the distance from the origin to the point.

Step 5 ：The sine of the angle is the ratio of the opposite side to the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side. The other three functions are the reciprocals of these.

Step 6 ：Calculate the values: \(x = 3.1622776601683795\), \(y = 2.449489742783178\), \(r = 4.0\)

Step 7 ：Calculate the trigonometric functions: \(\sin(\theta) = 0.6123724356957945\), \(\cos(\theta) = 0.7905694150420949\), \(\tan(\theta) = 0.7745966692414833\), \(\csc(\theta) = 1.6329931618554523\), \(\sec(\theta) = 1.2649110640673518\), \(\cot(\theta) = 1.2909944487358058\)

Step 8 ：Final Answer: The six trigonometric functions for the angle \(\theta\) are as follows: \(\sin(\theta) = \boxed{0.6123724356957945}\), \(\cos(\theta) = \boxed{0.7905694150420949}\), \(\tan(\theta) = \boxed{0.7745966692414833}\), \(\csc(\theta) = \boxed{1.6329931618554523}\), \(\sec(\theta) = \boxed{1.2649110640673518}\), \(\cot(\theta) = \boxed{1.2909944487358058}\)