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# Trigonometry

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

See attached file for full problem description.

### Complex Trigonometric Substitution

Given that e ^ jx + e ^ -jx e ^ jx - e ^ -jx Cos x = ----------------------, Sin x = -------------------- 2 2j using only this information, prove that Cos^2 x - Sin^2 x = 1 - 2 Sin^2 x

### Trigonometry and Vectors

A cable to the top of a tower makes an angle of 35 degrees with the level ground. At a point 100 yards closer to the tower the angle of elevation to the top of the tower is 59 degrees. Estimate the length of the cable. Approximate the angle between the vectors 4i-3J and 4i+3J

### Optimization: Minimizing Pipeline

Oil is being piped from an offshore oil well to a refinery on land. The shoreline is considered straight, the well is 2 miles out to sea (i.e, at a right angle to the shore), the refinery is 10 miles along the coast, underwater pipe costs \$360000/mile to construct, but the pipeline only costs \$260000/mile on land. Given this how

### 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

### Trigonometry: Phase Shift

Determine the phase shift of : Question 1 y = sin x Question 2 Y = sin(x -2 )

### Trigonometry: Period and Amplitude

Question 1 Determine the period of y=3 sin 2x Question 2 determine the amplitude y = -2 cos x

### Trigonometry: Sine and Range

Question 1 solve for x y=3sin x; for x =4pi Question 2 Determine the range of the following: y= -1/2 cos x

### Trigonometry : Amplitude

1. y=cos x; for x=4pi 2. Determine the Amplitude of: y = 3 sin x

### Trigonometry Word Problem: Right Triangles

Betty observed that the lamp post in front of her house casts a shadow of length 8 feet when the angle of inclination of the sun is 60 degrees. How tall is the lamp post? (In a 30-60-90 right triangle, the side opposite 30 is one-half the length of the hypotenuse).

### 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?

### System of Equations Dependent

Solve the system of equations: y = 3x -14 Y = 5x - 20 a. (-3,5) b. (3,5) c. Dependent d. Inconsistent Evaluate: 7 6 a. 5040 b. 42 c. 13 d. 7 See attached file for full problem description.

### Solve Using Trigonometric Substitution

Please solve for the following: Question: Use trigonometric substitution to evaluate: Integral (1/(sqrt(1 + x^2))) dx. Show all steps.

### 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

### Find the Lengths of the Side of a Triangle

The hypotenuse of a right triangle is 2.7 units long. The longer leg is 1.6 units longer than the shorter leg. Find the lengths of the side of the triangle.

### Trigonometry : Double Angle Formula

I need to verify this expression and I'm stuck... should I divide both sides by 2 first? Please advise as to the proper steps to take in this verification.

### 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

### Trigonometry - angles and sides

A triangle plot of land has sides of lengths 130 feet, 110 feet, and 100 feet. Approximate the smallest angle between the sides. A radar operator sights two objects, one at a distance of 7 miles and the other at a distance of 12 miles. If the angle between the sightings is 35 degrees, how far apart are the object? A

### Convert cis θ expression into trigonometric form.

Please see the attached file for the fully formatted problems.

### Finding the Sine of a Sum of Angles

If a and b are acute angles with Sin a =2/5squared and b = 1/5 squared, find the exact value of sin (a + b)

### 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