Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given point.
\[
(40,9)
\]
$\sin \theta=\square$ (Type an exact answer in simplified form.)
$\cos \theta=\square$ (Type an exact answer in simplified form.)
$\tan \theta=\square$ (Type an exact answer in simplified form.)
$\cot \theta=\square \quad$ (Type an exact answer in simplified form.)
$\sec \theta=\square \quad$ (Type an exact answer in simplified form.)
$\csc \theta=\square \quad$ (Type an exact answer in simplified form.)

Step 1 ：Given the point (40,9) on the terminal side of an angle in standard position, we can find the values of the trigonometric functions of the angle.

Step 2 ：The x-coordinate corresponds to the cosine of the angle, the y-coordinate corresponds to the sine of the angle, and the tangent of the angle is the y-coordinate divided by the x-coordinate.

Step 3 ：The cotangent, secant, and cosecant are the reciprocals of the tangent, cosine, and sine respectively.

Step 4 ：First, we calculate the distance from the origin to the point, which is \( r = \sqrt{x^2 + y^2} = \sqrt{40^2 + 9^2} = 41.0 \)

Step 5 ：Then, we can calculate the trigonometric functions as follows:

Step 6 ：\( \sin \theta = \frac{y}{r} = \frac{9}{41.0} = 0.22 \) (rounded to two decimal places)

Step 7 ：\( \cos \theta = \frac{x}{r} = \frac{40}{41.0} = 0.98 \) (rounded to two decimal places)

Step 8 ：\( \tan \theta = \frac{y}{x} = \frac{9}{40} = 0.23 \) (rounded to two decimal places)

Step 9 ：\( \cot \theta = \frac{1}{\tan \theta} = \frac{1}{0.23} = 4.44 \) (rounded to two decimal places)

Step 10 ：\( \sec \theta = \frac{1}{\cos \theta} = \frac{1}{0.98} = 1.03 \) (rounded to two decimal places)

Step 11 ：\( \csc \theta = \frac{1}{\sin \theta} = \frac{1}{0.22} = 4.56 \) (rounded to two decimal places)

Step 12 ：Final Answer:

Step 13 ：\( \sin \theta = \boxed{0.22} \)

Step 14 ：\( \cos \theta = \boxed{0.98} \)

Step 15 ：\( \tan \theta = \boxed{0.23} \)

Step 16 ：\( \cot \theta = \boxed{4.44} \)

Step 17 ：\( \sec \theta = \boxed{1.03} \)

Step 18 ：\( \csc \theta = \boxed{4.56} \)