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# Trigonometry

### Derivatives : Trigonometry Rate of Change Problems

1.) A fugitive is running along a wall at 4.0m/s. A searchlight 20m from the wall is trained on him. How fast is the searchlight rotating at the instant when he is 10m from the point on the wall nearest the searching? 2.) A balloon is rising from the ground at the rate of 6.0m/s from a point 100m from an observer, also on the

### Trigonometry Word Problems

A city block 500 feet by 500 feet has a large building 300 feet by 400 feet in the NW corner. The rest of the block is an unobstructed paved lot. What's the shortest distance from the SW corner to the NE corner of the city block, going through the paved lot (to the nearest foot)?

### Trigonometry Word Problems

To determine the distance to an oil platform in the Pacific Ocean from both ends of a beach, a surveyor measures the angle to the platform from each end of the beach. The angle made with the shoreline from one end of the beach is 83 degrees, from the other end 78.6 degrees. If the beach is 950 yards long, what are the distances

### Trigonometric Identities and Equations (26 Problems)

Trigonometry Questions. Please see the attached files for the fully formatted problems.

### Verify a Trigonometric Identity

Prove that sin2 x + cos2 x = 1 using only this information : Cos x = (e^jx + e^-jx)/2, sin x = (e^jx - e^-jx)/(2j) See attached file for full problem description.

### Trigonometry Word Problems

In mountain communities, helicopters drop chemical retardants over areas which approximate the shape of an isosceles triangle having a vertex angle of 38 degrees. The angle is included by two sides, each measuring 20 ft. Find the area covered by the chemical retardant.

### Trigonometry Word Problems

A ranger in fire tower A spots a fire at a direction of 295 degrees. A ranger in fire tower B, located 45 miles at a direction of 45 degrees from tower A, spots the same fire at direction of 255 degrees. How far from tower A is the fire? From tower B?

### Trigonometry problem: latitude and nautical mile

A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos 2P, where P is the latitude in degrees. a) Find the exact latitude (to 4 decimal places) of where you live, used to live, work, or used to work (include the zip code). The latitude fo

### Trigonometry Word Problems

1. A recent land survey was conducted on a vacant lot where a commercial building is to be erected. The plans for the future building construction call for a building having a roof supported by two sets of beams. The beams in the front are 8 feet high and the back beams are 6.5 feet high. The distance between the front and back

### Trigonometry Word Problems

A recent land survey was conducted on a vacant lot where a commercial building is to be erected. The plans for the future building construction call for a building having a roof supported by two sets of beams. The beams in the front are 8 feet high and the back beams are 6.5 feet high. The distance between the front and back bea

### Trigonometry : Pythagorean Theorem Word Problems

The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures &#8730;6m. Find the width and height.

### Trigonometry Exam (20 Problems)

Please see the attached file for all of the fully formatted problems. 1. You have calibrated your voltmeter so that you know a meter reading of 10 V is actually 10.2 V and a reading of 15 V is actually 15.6 V. What is the actual voltage when your meter reads 12.3 V? (1) 11.9V (3) 12.3 V (5) 13.1 V (2) 12.1 V (4) 12.7 V (6

### Tire Wear and Diameter; Trigonometric Identities and Equations

You interviewed an employee of an association representing the tire industry. The federal government mandates safety testing of all tires manufactured in the United States. Recently there has been concern that the rubber used in the tires could deteriorate while in store inventories. In September 2003, a safety group asked the U

### Graphs of Trigonometric Functions and Mean Value

(a) Sketch the graph of y = cos X in the range - &#960; &#8804; X &#8804; &#960;. &#960;="pi" Hence sketch the graph of y = cos X in the same range. (b) Find the mean value of y = cos X in the range - &#960; &#8804; X &#8804; &#960;

### Algebra and Trigonometry

See the attached file for full problem description. 16. The figure shows the graphs of f(x) = x^3 and g(x) = ax^3. What can you conclude about the value of a? a. a < -1 b. -1 < a < 0 c. 0 < a < 1 d. 1 < a 17. If f(x) = x(x+1)(x=4), use interval notation to give all values of x where f(x) > 0. a. (-1, 4) b. (-1, 0

### Length of a Rectangular Billboard

What is the length of the diagonal of a rectangular billboard whose sides are 5 meters and 12 meters? keywords: hypotenuse, Pythagorean

### Trigonometry Word Problem - Football Game

Suppose at kickoff of a football game, the receiver catches the football at the left side of the goal line and runs for a touchdown diagonally across the field. How many yards would he run? (A football field is 100 yards long and 160 feet wide).

### Trigonometry Word Problems

6) A right triangle is a triangle with one angle measuring 90Â°. In a right triangle, the sides are related by Pythagorean Theorem, c^2=a^2+b^2 , where c is the hypotenuse (the side opposite the 90Â° angle). Find the hypotenuse when the other 2 sides' measurements are 6 feet and 8 feet. 7) Suppose you travel north for 65 k

### Trigonometry and Heart Rates

#120 Digging up the street. A contractor wants to install a pipeline connecting point A with point C on opposite sides of a road. To save money, the contractor has decided to lay the pipe to point B and then under the road to point C. Find the measure of the angle marked x in the figure for exercise #120 on page 161.

### Trigonometric Identities and Factoring

Use trigonometric identities to factor and simplify the following: ? sin^2 x * sec^2 x - sin^2 x

### Trigonometric Identities

Match sin x sec x with one of the following: ? csc x ? tan x ? sin x tan x ? sin x cot x Use trigonometric identities to factor and simplify the following: ? sin2 x * sec2 x - sin2 x

### Trigonometric Functions

Which one of the following trigonometric functions of x is not correct? Which one of the following trigonometric functions of x is not correct given that sin x > 0 and sec x = -2? ? csc x = ( 2 sq rt 3) / 3 ? cos x = - 1 / 2 ? cot x = - ( sq rt 3 ) / 3 ? tan x = - ( sq rt 3 ) / 2

### Trigonometric Identities

Match sec4 y - tan4 y to one of the following: ? csc y ? sec2 y+ tan2 y ? 1+ tan y ? csc y x cot y

### Fixed and Variable Cost

Costs can be classified into two categories, fixed and variable costs. These costs behave differently based on the level of sales volumes. Suppose we are running a restaurant and have identified certain costs along with the number of annual units sold of 1000. Item: Raw Materials (cost for hamburgers) Total Annual Cost: 650

### Solving and Graphing Trigonometric Equations

Tan x = 3 cos x sec x = tan x = 3 csc^2x + sec x = 1

### Solving and Graphing Trigonometric Equations

2 cos^2 x + sin x + 1 = 0

### Trigonometric Identities Solved

Prove the identity of this problem. sin x - sin y x - y -------------- = tan (--------) cos x - cos y 2 keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

### Trigonometry: Finding the Limit

Evaluate the limit of sin[x])/x as x approaches 0. This is an example of a trigonometric function. Include all of the steps needed to reach the final answer.

### Transformations of Trigonometric Functions

Here is an example of the problem that I am working on at this time. I need to know how to list the transformation needed to change the graph of f(t) into the graph of g(t). f(x) = sin t; g(t)= -3 sin t

### Solving Trigonometric Equations Intervals

Solve each equation for solutions over the interval [0,2Ï€) sin x + 2 = 3 2 sec x + 1 = sec x + 3 Solve each eqation for solutions over the interval [0Âº,360Âº) cosÂ²Î˜ = sinÂ²Î˜ + 1 4cosÂ²Î˜ + 4cosÎ˜ = 1 See attached file for full problem description.