The point $(4,3)$ lies on the terminal side of an angle $\theta$. Find the exact value of the six trigonometric functions of $\theta$. \[ \sin \theta=\bigsqcup \] (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) \[ \cos \theta=\square \] (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) \[ \tan \theta=\square \] (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) \[ \csc \theta=\square \] (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) \[ \sec \theta=\square \] (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) \[ \cot \theta=\square \] (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) (1) Time Remaining: 00:56:23 Next

Step 1 ：To find the six trigonometric functions of the angle \(\theta\) whose terminal side passes through the point \((4,3)\), we first determine the hypotenuse of the right triangle formed by the x-axis, the y-axis, and the line segment from the origin to the point \((4,3)\).

Step 2 ：Using the Pythagorean theorem, the hypotenuse \(h\) is calculated as \(h = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5\).

Step 3 ：The sine of \(\theta\) is the ratio of the y-coordinate to the hypotenuse: \(\sin \theta = \frac{y}{h} = \frac{3}{5}\).

Step 4 ：The cosine of \(\theta\) is the ratio of the x-coordinate to the hypotenuse: \(\cos \theta = \frac{x}{h} = \frac{4}{5}\).

Step 5 ：The tangent of \(\theta\) is the ratio of the y-coordinate to the x-coordinate: \(\tan \theta = \frac{y}{x} = \frac{3}{4}\).

Step 6 ：The cosecant of \(\theta\) is the reciprocal of the sine: \(\csc \theta = \frac{1}{\sin \theta} = \frac{5}{3}\).

Step 7 ：The secant of \(\theta\) is the reciprocal of the cosine: \(\sec \theta = \frac{1}{\cos \theta} = \frac{5}{4}\).

Step 8 ：The cotangent of \(\theta\) is the reciprocal of the tangent: \(\cot \theta = \frac{1}{\tan \theta} = \frac{4}{3}\).

Step 9 ：Final Answer:

Step 10 ：\(\sin \theta=\boxed{\frac{3}{5}}\)

Step 11 ：\(\cos \theta=\boxed{\frac{4}{5}}\)

Step 12 ：\(\tan \theta=\boxed{\frac{3}{4}}\)

Step 13 ：\(\csc \theta=\boxed{\frac{5}{3}}\)

Step 14 ：\(\sec \theta=\boxed{\frac{5}{4}}\)

Step 15 ：\(\cot \theta=\boxed{\frac{4}{3}}\)