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# Trigonometry

### 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.

### Limit of Trigonometric Function : L'Hopital's Rule

Lim of theta as theta approaches zero of (cos theta - 1) / sin theta Please provide a detailed, step-by-step solution so that I can understand what is happening and will be able to solve similar problems in the future on my own. Thank you.

### 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 and vectors

A force of 800 lbs acts in an upward direction of 40 degrees with the floor. Draw this force as a vector and determine its horizontal and vertical components.

### 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?

### Trigonometry Distance Lengths

A length of rope 168 feet stretches from a bolt in the floor to the peak of an 87 foot radio tower. What is the distance from the floor at the radio tower base to the bolt? What angle does the rope make with the floor?

### Construct a one-to-one function

Problem: Construct a one-to-one function from (-1,2) into [0,1]. No need to prove.

### Trigonometric Differentiation

G(x) = (4-cos3x)/(x^2) Could you please include steps so that I may learn to do it myself? Thanks.

### Solve the Wave Equation

Show step by step work and explanation of the solution. (Answer is provided in the attachment.) Just #8, please.

### 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.

### Trigonometry : Solve the Triangle

Solve the triangle, if possible. B = 24.4° C = 102.9° b = 38.62 Which is the correct answer? A = 50.7°, a = 93.13, c = 76.37 A = 50.7°, a = 91.13, c = 74.37 A = 52.7°, a = 76.37, c = 93.13 A = 52.7°, a = 74.37, c = 91.13

### Trigonometry : Find the Missing Angle

Find the missing parts of the triangle. (Find angles to the nearest hundredth of a degree.) a = 162 yd b = 185 yd c = 323 yd Which is the correct answer? A = 19.99, B = 11.49, C = 148.52 A = 19.99, B = 22.98, C = 137.03 A = 22.98, B = 19.99, C = 137.03 No triangle satisfies the given conditions.

### Trigonometry - Angle and Distance

A plane flying a straight course observes a mountain at a bearing of 35.3° to the right of its course. At that time the plane is 9 km from the mountain. A short time later, the bearing to the mountain becomes 45.3°. How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km)?

### Trigonometry Word Problem: Angle and Distance

Starting at point A, a ship sails 24 km on a bearing of 211°, then turns and sails 33 km on a bearing of 302°. Find the distance of the ship from point A. Which is the correct answer? 57 km 73 km 16 km 40 km

### Finding the magnitude and direction angle of a vector

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. (√2,-1) Which one is the correct answer? √3; 305.3 3; 324.7 √3; 324.7 3; 125.3

### Applications of Trigonometry and Vectors

Please see the attached file for the fully formatted problems. 1. Find the indicated part of each triangle ABC. C = 118°, b = 130km, a = 75km; find c The correct answer to this problem is 180 km how did they come up with that answer? 2. Height of a Balloon: The angles of elevation of a balloon from two points A and B on

### Trigonometry Equation Interval Solution

Solve the equation for the interval [0, 2л). sin^2 x - cos^2 x = 0 Which is the correct answer? x = л/4, л/3 x = л/4, 3л/4, 5л/4, 7л/4 x = л/4 x = л/4, л/6

### Solving a Trigonometry Equation

Solve the equation for solutions in the interval [0, 360). cos 2x= √3/2 Which is the correct answer? x = 15, 165, 195, 345 x = 30, 90, 150, 270 x = 0, 120, 180, 240 x = 105, 165, 285, 345.

### Trigonometry

Find the exact value, given that sin A = -4/5 with A in quadrant IV tan 2A Which is the correct answer? - 7/24 24/7 - 24/7 7/24

### Trigonometry

Solve the equation for solutions in the interval [0, 360). tan 4x = 0 Which is the correct answer? x = 33, 57, 147, 237, 327 x = 0, 90, 180, 270 x = 0, 45, 90, 135, 180, 225, 270 x = 0, 45, 90, 135, 180, 225, 270, 315

### Inverse Circular Functions and Trigonometric Equations

1. Solve csc^2θ - 2 cot θ = 4 for solutions over the interval [0°, 360°]. Express approximate solutions to the nearest tenth of a degree. Could you please show me step by step to see how to get the correct answer? The correct answers are (18.4°, 135°, 198.4°, 315°)

### Trigonometry - Graphing a Function

Graph the attached function (which of the graph options are correct?)

### Trigonometry - Match Functions With Graphs

Match the attached functions with their graphs. Thank you.. Match the function with its graph. Which is the correct answer? 1) y = 1 + sin x 2) y = 1 + cos x 3) y = -1 + sin x 4) y = -1 + cos x A B C D 1A, 2D, 3C, 4B 1A, 2B, 3C, 4D 1A, 2C, 3D, 4

### How to Factor Trigonometric Expressions

Factor the trigonometric expression. Which is the correct answer? sin2x + sin2x cot2x cot2x - 1 sin2x + 1 cot2x + 1 1.

### Amplitude of Trigonometric Functions

Give the amplitude or period as requested. Which is the correct answer? Amplitude of y = 4 sin x 4л л/4 4 2л

### Trigonometric Identities; Exact Value

Use trigonometric identities to find the exact value of the attached equation. Which of the attached answers is correct?

### Unit circle proof

1) Prove from the unit circle that sin²&#8854; + cos²&#8854; = 1. Using the result describe the equation for which x = 3 + 2cos&#8854;, y = 1 + 3sin&#8854;. 2) Using problem one simplify sin²&#8854;/(1 + cos&#8854;) + sin²&#8854;/(1 - cos&#8854;)

### Trigonometric Identities

If you would please give me each step to solve these problems so I can get a better understanding how to solve these types of problems would be very helpful. Thanks. Graph each expression and use the graph to conjecture an identity. Then verify your conjecture algebraically. 1. sec x - sin x tan x Verify that each equat