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# Trigonometry

### Cartesian coordinates

1. A boat sails at a constant speed in a straight line. its position at time S is (30S- 300,10S +500). in the water there are two buoys, A and B. at positions A- (7100,2800) and B - (125700,42500). a) write an expression in terms of S that is the square of the distance between the boat and buoy A at time S, simplify the answe

### Pythagorean Triples Examples

What are Pythagorean triple? What are primitive Pythagorean triples? What is the Pythagorean triples theorem?

### Use trig. identities to transform one side of the equation

Use trig. identities to transform one side of the equation into the other. tan (data) + Cot (data) / tan(data) = csc^2

### Trigonometry and Triangles Word Problems

Points A and B lie in a direct line on level ground to the west of a mountain which is known to be 1 mile high. The angle of elevation from point A to the mountain top is 4 degrees and the angle of elevation from point B to the mountain top is 6 degrees. Find the distance between points A and B.

### Deriving trigonometric identities.

Use trigonometric identities to derive the following identities: a.) sin^2x+cos^2x=1 b.) sin2x=2sinxcosx c.) cos2x=cos^2x-sin^2x d.) cos2x=2cos^2x-1 e.) cos2x=1-2sin^2x

### Limit of cosine using epsilon/delta definition

I am having difficulty using the epsilon/delta definition....even difficulty when not using it. There's a problem which reads as follows: find the limit as x approaches 0 of (cosx-1)/x^2. The main reason as to why I am having difficulty without using the epsilon/delta definition is because I simply am confused what to do when

### Pythagorean Theorem

Find the side length x for a right triangle..when its sides are 7 and 11. Round to the nearest tenth

### Important information about application of trigonometric functions in real life

As a group, work together to submit the answers to the following problems. Use the Small Group Discussion Board to divide tasks, discuss strategies for solving problems, and check each other's work. The finished product should be one combined document for the entire group, showing all calculations and graphical representations u

### Trigonometric Limit

Find the trigonometric limit of the following (please show work) lim (x - tan2x)/sin2x x--> 0

### Finding Values of Trigonometric Expressions

Find the value of Trigonometric expression. 1) Cos [Sin^-1 (3/5)] 2) Cos [Tan^-1 (7/5)] See attached file for full problem description.

### Trigonometry: Find the Angle

See the attached file. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s , while the radius r = 1 meter and s = 300 centimeters. Find a positive angle less than 360degrees that is co terminal with the angle - 822degrees The minute hand of a clock is 5 inches long. Ho

### Trigonometry Word Problems

13) A rocket tracking station has two telescopes A and B placed 1.3 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket from telescope B at the moment when both tracking stations are directly east of the rocket telescope A r

### Trigonometry and Geometry Word Problems

3) A building 210 feet tall casts a 90 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 4 feet above ground level.) A) 66.40° B) 64.09° C

### Trigonometry and Vector Components Word Problems

See the attached file. 20. A small fire is sighted from ranger stations A and B. Station B is 1 .6 miles due east of station A. The bearing of the fire from station A is N40°E, and the bearing of the fire from station B is N5OW. How far, to the nearest tenth of a mile, is the fire from station A? 21. The magnitude and direc

### How far is the train from the crossing?

A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?

### Evaluating the Limit

(See attached file for full problem description).

### Identical to Cos

Which of the following is identical to cos(x +y)cos(x-y)?

### Right Triangle Trigonometry

Hos do I show calculations and graphical representations? (See attached file for full problem description WITH DIAGRAM) 1. Find the length L from point A to the top of the pole. 2. Lookout station A is 15 km west of station B. The bearing from A to a fire directly south of B is S 37°50' E. How far is the fire from B?

### Pythagorean Theorem

(See attached file for full problem description with diagrams) --- 1. A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including bas

### Trigonometric Equations

Find theta that satisfies the following equation: sin(2theta)sin(theta) = cos(theta)

### Trigonometry Applications Word Problems

You have been contacting cartographers and land surveyors to explore how they utilize graphs of functions in their work, and have learned that they create formulas to calculate size and mass. 1. A lobster boat is situated due west of a lighthouse. A barge is 12 km south of the lobster boat. From the barge the bearing to the lig

### Trigonometry Application Word Problems - Tire Wear, Trigonometric Equations and Identities

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

### Trigonometry for Oblique Triangles

1.-On the shore of the lake,a surveyor measured a straigth line of 30 meters between point A and B.what is the shortest distance between the point C on the island and the point A on the shore if angle C A B = 23degrees and 50 minutes and angle C B A =67 degrees and 28 minutes. 2.-Find the angle B in an oblique triangle in whi

### Trigonometric Equations and Identities

1. Solve each equation for the domain interval 0 less than or equal to x less than or equal to 2pie. Round the answers to the nearest hundredth of a radian, if necessary. a) 2cossquaredx+cosx=0 b) tansquaredx-1=0 c) 6sinsquaredx+sinx-1=0 2. Simplify each trigonometric expression. a) sinx (Suppo

### Value of Trigonometry Function

2. Find the value of the trigonometric function of 64 degrees 6 minutes 45 seconds. 3. If an a right triangle the sides a and b are known, the angle B equal to:

### Trigonometry and Pythagorean (Pythagorus) Theorem Problems

1.-In a right triangle with the hypotenuse c = 10 and the angle A =50 degrees ,what is the value of side b ? 2.- If in a right triangle the angle A = 40 degrees ,and the side a = 5,what is the value of side b ? 3.-If in a right triangle the hypotenuse c =12 and the side b = 5, what is the value of the angle A ? use natu

### Trigonometry Word Problems

A flagpole 5 m high stands on top of a building. From a point P on the street, the angle of elevation of the top of the pole is 32 degrees and the angle of elevation on the bottom of the pole is 30 degrees. How tall is the building? Solution Let AB represent the building (with point A on the street) and BC represent the

### Trigonometry: Sample Word Problem

A flagpole 5 m high stands on top of a building. From a point P on the street, the angle of elevation of the top of the pole is 32 degrees and the angle of elevation on the bottom of the pole is 30 degrees. How tall is the building?

### 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

### Trig

Latitude presents special mathematical considerations for cartographers. Latitude is the north-south location on the earth between the equator and the poles. Since the earth flattens slightly at the poles, a nautical mile varies with latitude. A nautical mile is given by N(e) = 6066 - 31 * cosine 2e. e represents the latitude in