Determine the exact value of the given function.

csc (7π/6)

The figure consists of two adjacent right triangles. Determine the exact values of w, x, y, and z.

Determine the missing side in the given triangle using the Pythagorean Theorem. Also, write the value of the six trigonometric ratios for angle P.

p = 12, q = 37

Solve the following trigonometric equation. Consider all the angles as acute angles.

sin(5α + 18°) = cos(4α - 27°)

Determine the exact value of the given trigonometric function.

sec 30°

A large clock is displayed at a market in Barcelona, Spain. Calculate the linear speed v of the tip of its minute hand if the hand has a length of 50 cm.

A prototype of a car wheel has a diameter of 15 cm. During testing, it rotates at 750 times per minute. Calculate the linear speed v of a point on the outermost surface of the car wheel.