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# Trigonometry

### Distance Formula in 2- and 3-Dimensional Space

Explain how to derive the formula for the distance between two points in analytic geometry in 3-space. (list each necessary step and describe all terms used). Also to discuss how the Pythagorean theorem helps to find distances in 2 and 3 dimensions. Provide at least three examples of how the distance formula can be used in real

### History, Definition, and Calculations of Pythagorean Theorem

1) The numbers 3, 4, and 5 are called Pythagorean triples since 3 2+ 4 2= 5 2. The numbers 5, 12, and 13 are also Pythagorean triples since 5 2 + 12 2= 13 2. Can you find any other Pythagorean triples? Actually, there is a set of formulas that will generate an infinite number of Pythagorean triples. 2) Select at least 5 more

### Geometry and Trig Questions

Set 1 11: The actual definition of the word tangent comes from the Latin word tangere, meaning "to touch" in mathematics the tangent line touches the graph at a circle at only one point and function values of tan ѳ are obtained from the length of the line segment tangent to a unit circle. Can the line segment ever be greater t

### Use the chain rule to find dy/dx of trigonometry function

Dear People, Please list all steps even the ones that seem obvious. I was able to do the following problem but I'm unable to do the next one. This is the problem that I was able to do. Use the Chain Rule to find dy/dx The problem is the one that I'm having problems with. I don't understand how to differentiate Dx u s

### Trigonometry Word 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 full credit. Work shown here:

### Trig

2 - 3 paragraphs Details: 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 ri

### The following chart shows some common angles with their degrees and radian measures.

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: 2. An A-frame lake house is 21 feet wide

### Trigonometry : Angle Conversions and Word Problems

MTH212 Unit 5 Assignment : Please see the attached file for the fully formatted problems. 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. 2.

### Importance of Teaching Geometry

The importance of geometry's role in the math curriculum is debated in many high schools and colleges. Some schools offer the course while others have done away with it. Based on what you have learned within this unit, do you think geometry is a valuable tool for students to learn? Choose one side of this debate, state your view

### Trigonometry, Area, Volume and Word Problems - MTH212 Unit 4

1. Along a straight shoreline, two lighthouses, A and B, are located 2000 feet apart. A buoy lies in view of both lighthouses, with angles 1, 2, and 3 as indicated. (Angle 1 is denoted by , angle 2 is denoted by , and angle 3 is denoted by .) A. By looking at the picture, do you think is an acute, obtuse, right, or a

### Trigonometry Word Problems: The Rate of Change of an Angle

Please see the attached file for the diagram associated with this problem. Question: An airplane is flying at an altitude of 8 miles towards a point directly over an observer. If the speed of the plane is 615 miles per hour, find the rate at which the angle of observation, theta, changing by at the moment when the angle is 2

### Trigonometry, Algebra, & Geometry

1. To raise money, the local baseball teams decided to sell team logo hats (H) and T-shirts (T). The league director decided to hold a contest among the teams to see which team can raise the most money. The contest lasted for 3 weeks. Here are the results of the first 2 weeks. The numbers represent the number of hats and T-shirt

### Algebra and Trigonometry - 20 Problems

Michelle reads 1,200 words in 7 minutes, and Tricia reads 700 words in 3 minutes. Who is the faster reader? Find the unit price for the item: \$6.96 for a dozen pears. Is the rate equivalent to the rate ? Solve for the unknown: A basketball player scored

Measure the height of your computer monitor to the nearest tenth of a centimeter or sixteenth of an inch. Measure the width of your monitor as well. Use the Pythagorean theorem to find the length of the diagonal of your monitor. In your post, include the height, the width, and the calculations needed to determine the length of

### Remaining Trigonometry Ratio

See attached Find the remaining trigonometric ratio: Prove the identities: Evaluate the expression: Find all values of x in the interval [0, ] that satisfy the equation: Graph the function:

### Trigonometry - Oblique Triangles

1. Two diagonals of a parallelogram are 48 ft and 37 ft respectively. If they intersect at 40°, find the sides of the parallelogram. 2. A flagpole stands vertically on a 13° 25' slope. 500 feet downhill from its base its top is sighted at an elevated angle of 27° 30'. Find its height. 3. Town B is 9 miles northwest of t

### Question about Mathematics - Trigonometry

Please help with the following problem. Provide a step by step solution along with diagrams. Draw the oblique triangle, classify each oblique triangle according to the four cases and solve for the required side or angle: 1. if b = 12, c = 15 and C = 67°, find a. 2. if a = 12, b = 7 and c = 5, find A. 3. if a = 25,

### Mathematics - Trigonometry - Trigonometric Functions

How do you figure out trigonometric functions?

### Trigonometry : Distance of Ladder from Wall, Angle from Diagonal

2. The angle of elevation of a 15-ft ladder is 70°. Find out how far the base of the ladder is from the wall. 3. A diagonal is drawn in a 12-in, square floor tile. Find the sine, cosine, and tangent of the angle formed by the diagonal and a side. 9. A gutter cleaner wants to reach a gutter 40 ft above the ground. Find the

### Pythagorean Theorem

Two vertical poles 10 ft apart are both 10 ft tall. Find the length of the shortest rope that can reach from the top of the one pole to a point on the ground between them and then to the top of the other pole.

### Prove the identity and find f(x)

Please see the attached file. 7. (i) Prove that cosh 2 2 sinh2 &#61553;+ 1 (ii) A chain hangs in a shape called a catenary, the equation of which is f(x) = a cosh ( / a) Determine the value of x when f(x) = 48 and a = 35.

### Seveal Examples of Solving Trigonometric Equations

Find all real numbers in the interval [0, 2pi] that satisfy these equations (see attached) 15. sin^2a - sqrt(2)/2 sina = 0 16. 6cos^2a - 7cosa + 2 =0 17. 6sin^2a - 2sina - 1 = 0.

### Word problem: Pythagorean Theorem

Fran works due north of home. Her husband Ben works due east. They leave for work at the same time. By the time Fran is 3 miles from home, the distance between them is one mile more than Ben's distance from home. How far from home is Ben? Be is __ miles from home?

### Proving Trigonometric Indentities

Attached are the problems that I can not find identities for. 1) (3sin^2x+sinx-4)/-cos^2x = (3sinx+4)/sinx+1 2) sin(x+pi) = -sinx

### Trigonometry Functions for a Positive Acute Angle

Please answer all attached questions with full solutions, working and answers. Thank You. Express each of the following trigonometric functions in terms of the same function of a positive acute angle. Convert to radians, expressing your answers as a multiple of pi . Convert to degrees. A horizontal section of a circular p

### Trigonometric Ratios : Triangles and Word Problems Please see the attached file for the fully formatted problems

Please see the attached file for the fully formatted problems. 1. Express 59 degrees 21 minutes as (i) degrees in decimal form. (ii) radians. 2. Find a value for O if sinO 0.4 and 0 900. 3. In the triangle at right, find values for: (i) sin o (ii) tan o (iii) cosec o 5. The owner of a restaurant must build a

### Pythagorean triples

There is a set of formulas that will generate an infinite number of Pythagorean triples. Please find at least five more in addition to 3, 4 , 5 12, and 13, and show why your 5 sets of Pythagorean Triples work in the Pythagorean Theorem formula. Please solve the following problem and provide detail steps?

### Trigonometric identities and equations

Please see the attached file Q1. Prove the identity cos3t = 4cos^3t- 3cost Q2. Prove the identity: (cos3a - cos7a) / (sin7a + sin3a) = tan2a Q3. Solve the equation, giving answer in radians in the range 0 to 2 pi sin(2t) -1 = cos(2t)

### Trigonometric identities expressed

Express tan 2A in terms of tanA and hence solve for 0 < A < 180, the equation tan2AtanA = 8.

### Finding length through Pythagorean Theorem

For the following right triangle, find the side length . Round your answer to the nearest tenth.