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# Trigonometry

### 15 Trigonometry Problems : Angular Velocity, Shadows, Waves and Triangles

Trigonometry Review 1. Assume the angle of inclination of the sun is given by Theta = (pi/12)t, where t is the number of hours after sunrise. Suppose we have a 10 meter high flagpole. a. What is the angular velocity of the sun? b. Write an equation for the length of the flagpole's shadow when the angle of the sun is theta rad

### one-dimensional wave equation for a semi-infinite string

Find the solution to: PDE: u*xx-c(to the power of negative k)u*tt=0 , 0 ICs: u(x,0)=f(x) and u*t(x,0)=g(x), x>=0 BC: u*x(0,t)=0 , t>=0 This BC corresponds to a string with its end point free to move in a vertical direction. (Please remember to include to boundary condition in your solution. Thanks very much!)

### Vibrating String and d'Alembert's Solution in Wave Equation

2. Show that, like the wave equation, the given PDE is hyperbolic and find its general solution by introducing the suggested change of variables. (b) uxx - 4uxy - 5uyy = 0 ........ Please see the attached file for the fully formatted problems.

### 10 Trigonometry Application Word Problems: Angles and Lengths

See the attached file. 1. Suppose that a boat leaves Jacksonville traveling at a bearing of 110o. It goes 30.0 km, and then travels 100.0 km at a bearing of 170o. How far is it from Jacksonville? 2. Suppose that I am trying to judge the distance across a lake. I stand facing some house on the opposite shore. I turn 95o to the

### Statistics (10 Problems) : Hypothesis Testing, Chi-Square, Nonparametric Tests and Mann-Whitney U-Test

2. A researcher randomly selects a sample of college students majoring in physics, chemistry, psychology, P.E., or English lit. He notes each student's major subject, and also whether that student is a blonde, a brunette, or a redhead. The data are as follows: Physics Chem Psych P.E. English Total Blonde 8 10 20 4 10 52

### Even and Odd Function

5. Determine fe(x) and fo(x). Is f even? Odd? Neither? - See attachment. (g) x^4 + x^3 + x^2 + x + 1 (j) sin(sin x) (k) cos(sin x) (^ is raised to the power of) fe(x) means even function. fo(x) means odd function.

### Identities of Plane Trigonometry

Important Formulas and their Explanations (VI): Identities of Plane Trigonometry Pythagorean Relation Pythagorean Identities Pythagorean Identities

### Trigonometric expressions simplified

1) 2 tan (theta /2)= 2) 2 tan theta Sin ^2 (theta /2)= 3) 2 Cos (45 + x) Cos (45-x)= 4) (Sin 3 x - 3 Sin x )/ ( Cos 3 x + 3 Cos x) = 5) 2 tan (theta /2) / { 1 + tan ^2 (theta /2) } = 6) Find the least positive value of theta such that tan (45+ theta ) - 3 tan theta =2

### Trigonometry Application Word Problems : Matrices, Incline, Magnitude and Area

Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can be

### Trigonometry Word Problems : Tan Function

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 lighthouse is 63 degrees (12 km is the length of the side adjacent to the 63 degree bearing). How far is the lobster boat from the light house? 2. A recent land survey was conducted on a vacant

### Trigonometry questions

I am pretending that I am interviewing for a position with 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

### Trigonometry and nautical miles

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

### Right angle trigonometry

A V-gauge is used to find the diameters of pipes. Look at the figure in the attachment, the measure of angle AVB is 54°. A pipe is placed in the V-shaped slot and the distance VP is used to predict the diameter. a. Suppose that the diameter of a pipe is 2 cm. What is the distance VP? b. Suppose that the distance VP is 3.9

### Trigonometric equations

Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles. The diameter of the wheels of one car is 15 inches. The diameter of the wheels of the other car is 16 inches. If the tires are equally durable and differ only by diameter, which car will probably need new tires first? Why? Explain

### Trig Identifies and Equations: Tangent Sum Formulas and Tire Circumferences

1. Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles. The diameter of the wheels of one car is 15 inches. The diameter of the wheels of the other car is 16 inches. If the tires are equally durable and differ only by diameter, which car will probably need new tires first? Why? 2

### Evaluate the Integral

Evaluate (be careful if n=m) &#8747; 0 --> L sin(n pi x/L) sin(m pi x/L) dx for n>0 and m>0. Use the trigonometric identity 2 sin a sin b = cos(a-b) - cos(a+b) Please see the attached file for the fully formatted problems.

### Sound Waves

Consider the wave equation when the solution s admits spherical symmetry, ie, s(t,x,y,z)=v(t,r), where ... , the wave equation becomes: (1) making the substitution for some twice differentiable function h, show that (1) becomes hence, show that the general solution reads for any twice differentiable functions f

### An Equilibrium and Weight Problem

Two builders carry a sheet of drywall up a ramp. The drywall is very thin and is 3.20m long and 2.20m wide. The ramp makes an angle of 18.0 degrees with the horizontal. The lead builder carries a weight of 139.0 N (31.2 lb). What is the weight carried by the builder at the rear if the drywall is carried by the longside (distan

### Green's Functions, Wave Equation, Heaviside Function and Neumann Boundary Condition

The Green's function for the infinite domain is... where H is the Heaviside function. Use Green's functions to solve the Neumann boundary condition problem... Give explicit formulas for the solution in each region x>t and x<t. Please see attached for equations.

### Sine or Cosine Curve Versus a Tangent Curve

What are the differences in the steps of graphing a sine or cosine curve vs. a tangent curve? Please provide answer in written form not graphical form.

### Trigonometric Equations : Solution and Area of Triangle

1. Find all the solutions of the equation 3sin20(degrees) = cos2x(degrees) in the range 0(degrees) is less then or equal to x(degrees) which is less than or equal to 180(degrees). 2. A triangle has sides A-C =3cm A-B = 5 cm B-C = 4 cm Find the area of

### Prove the trigonometric identity.

Prove that [sin &#952;/(1 - cos &#952;)] - [(1 + cos &#952;)/sin &#952;] =0 Provide reasons (identities, operations, etc.) for each step in the proof. Include any thoughts, ideas or strategies used to prove the identity.

### Function indicated domain of definition

The problems are from complex variable class. Please specify the terms that you use if necessary and explain each step of your solution. If there is anything unclear in the problem, please tell me. Thank you very much. 4. Use the given theorem to show that each of these functions is differentiable in the indicated domain of

### angle of elevation should be used to hit an object 190 meters

A gun has a muzzle speed of 80 meters per second. What angle of elevation should be used to hit an object 190 meters away? Neglect air resistance and use g= 9.8 as the acceleration of gravity.

### Hyperspheres : Volume of a Sphere with Radius 'r'

Finding formulas for the volume enclosed by a hypersphere in n-dimensional space. a) Use a triple integral and trigonometric substitution to find the volume of a sphere with radius r.

### Trigonometry : Word Problems

Q1. A glass crystal sculpture is made in the shape of a regular octagonal prism with 10 cm sides. Each of the lateral faces is square. To avoid breakage in shipment, the piece is padded with plastic foam beads when it is packed in its square-based rectangular box. The layer of beads must be at least 1 cm thick on all sides of

### TRIGONOMETRY

A handicap ramp is 5.26 meters above the ground. What will the length of the ramp if it makes an angle of 23 degrees with the floor?

### What is the angle the beam makes with the wall?

A beam 25 feet long leans against a wall. If the top of the beam rests at a point on the wall 17.5 feet above the floor, what is the angle the beam makes with the wall?

### Measure Height of Mountain : Angle of Elevation

To measure the height of a mountain a surveyor takes two sightings of the peak at a distance of 900 meters apart on a direct line to the mountain (see attached picture). The first observation results in an angle of elevation of 47 degrees, whereas the second results an angle of elevation of 35 degrees. If the transit is 2 meters

### Trigonometry Question: Solving the Triangle

Solve the triangle, if possible. C = 35°30' a = 18.76 c = 16.15 Which is the correct answer? A = 42°25', B = 102°05', b = 25.19 No solution A = 42°25', B = 102°05', b = 27.20; A' = 137°35', B' = 6°55', b' = 3.35 A = 102°05', B = 42°25', b = 17.52; A' = 6°55', B' = 137°35', b' = 26.19.