# Trigonometric Functions

## The Tide in Bay of Fundy: The Depths of High and Low Tides

**Problem**

The tide in Bay of Fundy rises and falls every 13 hours. The depth of the water at a certain point in the bay is modeled by a function *d* = 5 sin (2π/13)*t* + 9, where *t* is time in hours and *d* is depth in meters. Find the depth at *t* = 13/4 (high tide) and *t* = 39/4 (low tide).

- The depth of the high tide is 15 meters and the depth of the low tide is 3 meters.
- The depth of the high tide is 16 meters and the depth of the low tide is 2 meters.
- The depth of the high tide is 14 meters and the depth of the low tide is 4 meters.
- The depth of the high tide is 17 meters and the depth of the low tide is 1 meter.

## Length of one side for maximum area of trapezoid (solution by Calculus)

## 45 - Angle of elevation of the the kite's cord

**Problem 45**

A kite is 60 ft high with 100 ft of cord out. If the kite is moving horizontally 4 mi/hr directly away from the boy flying it, find the rate of change of the angle of elevation of the cord.

## 44 - Angle of elevation of the rope tied to a rowboat on shore

**Problem 44**

A rowboat is pushed off from a beach at 8 ft/sec. A man on shore holds a rope, tied to the boat, at a height of 4 ft. Find how fast the angle of elevation of the rope is decreasing, after 1 sec.

## 40 - Base angle of a growing right triangle

**Problem 40**

The base of a right triangle grows 2 ft/sec, the altitude grows 4 ft/sec. If the base and altitude are originally 10 ft and 6 ft, respectively, find the time rate of change of the base angle, when the angle is 45°.

## 26-27 Horizontal rod entering into a room from a perpendicular corridor

**Problem 26**

A corridor 4 ft wide opens into a room 100 ft long and 32 ft wide, at the middle of one side. Find the length of the longest thin rod that can be carried horizontally into the room.

## 24-25 Largest rectangle inscribed in a circular quadrant

**Problem 24**

Find the area of the largest rectangle that can be cut from a circular quadrant as in Fig. 76.

## 23 - Sphere cut into a pyramid

**Problem 23**

A sphere is cut in the form of a right pyramid with a square base. How much of the material can be saved?

## 22 - Smallest cone that may circumscribe a sphere

**Problem 22**

A sphere of radius *a* is dropped into a conical vessel full of water. Find the altitude of the smallest cone that will permit the sphere to be entirely submerged.