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# Trigonometry

### Trigonometry : Angles and Lengths

MTH212 Unit 5 Individual Project - A 1. The following chart shows some common angles with their degrees and radian measures. Fill in the missing blanks by using the conversions between radians and degrees to find your solutions. Show all work to receive full credit. Work shown here:

### Trigonometry has many applications in the real world. One particular area in which it can be used is in architecture.

Trigonometry has many applications in the real world. One particular area in which it can be used is in architecture. If you were an architect, describe a specific situation in which you could use right triangle trigonometry to help you design a new hospital. Give a specific example and explain how right triangle trigonometry co

### Transformations of Graphs of Trigonometric Functions

Describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. 43. y=0.5 sin 3x How do you come up with the following answer? starting from y=sinx, horizontally shrink by 1/3 and vertically shrink by 0.5 45. y= -2/3 cos x/3 How do you come up with the following answer? s

### Trigonometry and Plotting Trigonometric Equations

Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 5.7 centimeters and the radius of the larger wheel is 18.1 centimeters. Through how many degrees will the larger wheel rotate if the smaller one roatates 151 degrees? ans. 47.55 deg

### Trigonometry

Please see the attached file for the fully formatted problems. MTH212 Unit 5 Individual Project - A 1. The following chart shows some common angles with their degrees and radian measures. Fill in the missing blanks by using the conversions between radians and degrees to find your solutions. Show all work to receive fu

### Trigonometric Identities, Solving Triangles, Focus, Directrix, Sequences , Sums and Derivatives

Complete the identity (see attached) a. sin q tan q b. -2 tan 2q c. 1+cot q d. sec q + csc q Complete the identity. Sin(a+b) cos b - cos(a+b) sin b a. sin a b. sin a b-sin a b c. 2 sin b cos b(sin a - cos a) d. sin a cos b - cos a sin b Solve the triangle. Round lengths to the nearest tenth and angle meas

### Slope of Incline, Power and Energy

A. A tank of mass 80 metric tons is travelling at a uniform speed of 54 KM/hr on a level terrain. It then starts travelling uphill on an incline of 1 in 10 (sine slope). Calculate the extra power required from the engine in megawatts to maintain the same speed on the incline. b. When it has travelled 100m up the incline the d

### Speed Unit Conversions

1540 mm/microseconds = ___________ m/s 1 X 10^5 cm/mlliseconds = _______1050____ m/s If a sound wave travels through soft tissue at a velocity of 1.54 mm/microsecond for 2203 ms, How far has the sound wave traveled using the echo-ranging formula d=ct, where d= distance, c= velocity, t= time Using the same formula

### Use common trigonometric identities for the functions given to find the indicated trigonometric functions.

See attached file for full problem description.

### History of Mathematics : Square and Triangular Numbers and the Pythagorean Theorem

Figurative Numbers & Pythagorean Theorm. See attached file for full problem description. 9) Which basic trigonometric identity is actually a statement of the Pythagorean Theorem? Justify your answer. 5) From very early on, mathematicians were interested in finding right triangles whose sides had integer length. By the Pythag

### Pythagorean theorem and sin rule

1) Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. A=23 degree B=21 degree a = 42.8 (2) The distance from home plate to dead center field in Sun Devil Stadium is 401 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it fro

### A man holds a 178 N ball in his hand, with the forearm horizontal (see the drawing). He can support the ball in this position because of the flexor muscle force M, which is applied perpendicular to the forearm. The forearm weighs 20.2 N and has a center of gravity as indicated. (a) Find the magnitude of M. (b) Find the magnitude and direction of the force applied by the upper arm bone to the forearm at the elbow joint.

A man holds a 178 N ball in his hand, with the forearm horizontal (see the drawing). He can support the ball in this position because of the flexor muscle force M, which is applied perpendicular to the forearm. The forearm weighs 20.2 N and has a center of gravity as indicated. (a) Find the magnitude of M. (b) Find the m

### Functions: Discontinuities, Trends and Forecasting

1) What is a discontinuity? How are discontinuities found? Which types of graphs are continuous? 3) If Bob starts off with a salary of \$50,000 and earned \$1000 a year for his salary, give the equation of his salary, S, for year t. Use this equation to find the year in which he would be earning \$56,400. Show all your work usin

One force is pushing an object in a direction 50 degree south of east with a force of 25 Newton. A second force is simultaneously pushing the object in a direction 70 degree north of west with a force of 60 Newton. If the object is to remain stationary, give the direction and magnitude of the third force which must be applied to

### Trigonometry Word Problems and Geometry

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? 3. The wheels of a car have a 24-in. diameter. When the car is being driven so that the wheels make 10 revolutions per se

### Area and Volume Word Problems

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of

### Dimensions of the Door

Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilize the door by attaching a steel cable diagonally. If the cable measures sq 194/2 ft, what are the dimensions of the door?

### Trigonometry : Tire Wear, Equations and Identities and Tangent Functions

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 Word Problems

Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? North and east can be considered the directions of the y- and x-axis respectively. Round to the tenth decimal place. A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides

### Trigonometry Questions

Give a polar equation for the curve whose graph is a vertical line that passes 3 units to the right of the origin. A parabolic reflector has a width w=20 feet and a depth d =4 feet. how far from the center will the focal point be? See attached for third question

### Trigonometry Questions

Solve the system x-2y+z=-1 and system x+2y-2z=-1 -2x+3y+2z=4 x+3y+z=10 2x+y+3z=9 2x+6y+2z=20 Find the maximum value of c=6X + 5y on the region determined by the constaints 3x+2y+>or equal to 20 2< or equal to X<or equal to 8 1< or eq

### Pythagorean theorem formula

Calculate the hypotenuse of a right-angled triangle. The Pythagorean theorem. The application should also allow the user to perform a cylinder volume calculation. Pythagorean theorem formula: a2 + b2 = c2 Cylinder volume formula: Cylinder volume = r2 h Allow the user to enter the value of "a" and the value of "b"

### 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

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.

### 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