Find the value of each of the six trigonometric functions of the angle $\theta$ in the figure.
\[
a=20 \text { and } b=15
\]
$\sin \theta=$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression
\[
\cos \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.
\[
\tan \theta=\frac{3}{4}
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
\[
\csc \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
\[
\sec \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
\[
\cot \theta=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Step 1 ：Given that the sides of a right triangle are a = 20 and b = 15, we can calculate the hypotenuse c using the Pythagorean theorem: \(c = \sqrt{a^2 + b^2} = \sqrt{20^2 + 15^2} = 25.0\)

Step 2 ：The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, \(\sin \theta = \frac{b}{c} = \frac{15}{25} = 0.6\)

Step 3 ：The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. So, \(\cos \theta = \frac{a}{c} = \frac{20}{25} = 0.8\)

Step 4 ：The tangent of an angle is the ratio of the sine of the angle to the cosine of the angle. So, \(\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.6}{0.8} = 0.75\)

Step 5 ：The cosecant, secant, and cotangent are the reciprocals of the sine, cosine, and tangent, respectively. So, \(\csc \theta = \frac{1}{\sin \theta} = \frac{1}{0.6} = 1.67\)

Step 6 ：\(\sec \theta = \frac{1}{\cos \theta} = \frac{1}{0.8} = 1.25\)

Step 7 ：\(\cot \theta = \frac{1}{\tan \theta} = \frac{1}{0.75} = 1.33\)

Step 8 ：Final Answer: The six trigonometric functions of the angle \(\theta\) are as follows: \(\sin \theta= \boxed{0.6}\), \(\cos \theta= \boxed{0.8}\), \(\tan \theta= \boxed{0.75}\), \(\csc \theta= \boxed{1.67}\), \(\sec \theta= \boxed{1.25}\), \(\cot \theta= \boxed{1.33}\)