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# Trigonometry

### 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

### Period, Amplitude, Range, Y-intercept and Phase Shift

Develop the solutions for the following problems: 1.) Graph the function y = -1 + 2sin(x + &#960;) over a 2-period interval. a. What is it's period? b. What is its amplitude? c. What is it's range? d. What is the y-intercept of it's graph? e. what is it's phase shift? 2.) The formula for the up and down motion o

### Trigonometry : Word Problem

From a boat on the lake, the angle of elevation to the top of a cliff is 16° 10' If the base of the cliff is 1216 feet from the boat, how high is the cliff (to the nearest foot)? Which is the correct answer? 353 ft 356 ft 366 ft 363 ft

### Trigonometry : Tan of an Angle

Use a calculator to find the function value. tan 63 degrees 44'

### Trigonometry : Word Problems

Please see the attached file for the fully formatted problems. Find the exact trigonometric function value. sec 2655 Solve the problem. From a boat on the lake, the angle of elevation to the top of a cliff is If the base of the cliff is 1216 feet from the boat, how high is the cliff (to the nearest foot)? Solve the

### How to Use Trigonometric Identities and Periodicity

Find the value of x (in degrees) for: cos(6x+5) = 1/sec(4x+15) sec(2x+6)*cos(5x+3)=1. See the attached file.

1. If cos θ = 4/5 and θ is in quadrant IV, find the values of the trigonometric functions of θ. 2. Suppose θ is in the interval (90º, 180º). Find the sign of each function value. (a) cos θ/2 (b) cot(θ - 180º) 2. Use the reciprocal, quotient, and Pythagorean identities to give three expressions that complete t

### Using Trigonometry to Calculate Angles of a Triangle

See attached file.

### Trigonometry - Draw a ray

Locate each point in a coordinate system. Draw a ray from the origin through the given point. Indicate with an arrow the angle in standard position having smallest positive measure. Then find the distance r from the origin to the point, using the distance formula. (4&#8730;3, -4)

### How long is the wire if the pole and building are 48' apart and the ground is level?

An overhead wire stretches from the service drop on a building, which is 20' from the ground, to an insulator on a pole which is 35' from the ground. How long is the wire if the pole and building are 48' apart and the ground is level? Carry the answer out 2 decimals.

### Trigonometric equation

Tan x + sec x = 1 Solve equation for 0 less than or equal to X less than 2 pi

### Trigonometry (Angles and Distance)

A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string have been let out?

### Pythagorean Theorem Word Problem

"There is a bamboo 10 ft. high, the upper end of which being broken reaches the ground 3 feet from the stem. Find the height of the break." Please show your work in steps so I can understand the process used to solve it.

### Problem Involving Derivatives of Trigonometric Functions

Please see the attached file for the fully formatted problems. Find derivatives of these functions chosing appropriate methods: a) f(x) = 4x3 - 2x cos x b) g(x) = (x-2)3(x2+2x+1)3 sin2x / (x-1)2(x2+4) c) h(t) = sin (2t2 -6)

### Trigonometric Formula Square Root

Using the exact value cos(pi/4) = 1/square root of 2 and a trigonometric formula, show that sin (pi/8) = (square root of (2 - Square root of 2)/2. Using exact value cos(pi/6) = (square root of 3)/2 and a double angle formula to obtain an expression for the exact value of sin(pi/12)

### Solving for Angle Beta (Trigonometry Problem - Type IV)

In the attached problem I need to solve for the unknown angle Beta. The book calls it a type IV problem and gives the procedure on how to solve for a type IV problem. I have tried to solve this problem but with no luck. I have attached the problem, the procedures to solve for the type IV and the formulas and pictue of a type I

### Trigonometric Functions Solved

Solve this trigonometric equation for x where 0<x<2pi 2sin^2x + 3cos x = 0

### Slid Trigonometry : Type II Pyramid

This triangular pyramid is a type II as the book puts it. Three faces are right triangles and the 4th in a diagonal plane is an oblique triangle. The book explaines that if the angle to be found is in the oblique triangle you should solve for an auxilliary angle in the third right angle which lies at the same vertex as the requi

### Differentiation of Inverse Trigonometric Functions

Angular rate of change: A television camera at ground level is filming the lift-off of a space shuttle at a point 750 meters from the launch pad. Let (theta) be the angle of elevation of the shuttle and let s be the distance between the camera and the shuttle. Write (theta) as a function of s for the period of time when the shut

### Wave Equations : Comparison Between Circular and Square Vibrating Membranes

Please see the attached file for the fully formatted problems. Consider a circular membrane of radius a and a square membrane Assume the two membranes (i) have the same area. .... (ii) obey the same wave equation... (iii) Have the same boundary conditions phi = 0 at their boundaries. A) TABULATE (i) the 3 lowest frequen

### Properties of Neumann functions

Show that For Neumann function of the n'th order: N_[-n] = (-1)^n*N_[n]

### Wave Periodic Extension Equation

Wave equation problem - show that the wave eq. u(x,t) can be expressed as 1/2((fodd(x+ct)+fodd(x-ct)) - fodd being the odd periodic extension of f(x) See attachment

### Trigonometric Expressions

Please see the attached file for the fully formatted problems. 1.)Calculate: 234.1sin(1.56)/cos(.34) 2.) Is the following even or odd? Cos(sin t)

### Periodic Functions via Convolution

Please see the attached file for the fully formatted problems. "Periodic Function via Convolution" Consider the periodic train of Dirac delta "functions" f(x) =.... with real period .... (a) FIND and DESCRIBE its Fourier transform F(k). What happens to F if c gets doubled? (b) Let p(x + c) = p(x) be a periodic function.

### Wave Packet Trains: Express in Terms of Dirac Delta Function

Please see the attached file for the fully formatted problems.

### Volume of a Hypersphere : n-Tuple Integral

Please do #4. Please see the attached file for full problem description. In this project, we find formulas for the enclosed by a hypersphere in n?dimensional spaces 1 Use a double integral, and trigonometric substitution, together with Formula 64 in the Table of Integrals, to find the area of a circle with radius r 2 U

### Solve conditional trigonometric equation (between 0 and 360)

Cos2(Theta)-2sin^2(Theta)=-2

### Prove a Trigonometric Identity

2tan(X)/1+tan^2(X)=sin2(X)

### Using triangle ABC, show that form is able to find side lengths.

Let ABC be a triangle. Prove that (cos(A/2))^x, (cos(B/2))^x, and (cos(C/2))^x are the lengths of a triangle for any x greater than or equal to 0. From what I have found in my books, it is impossible to solve for side lengths of a triangle using AAA b/c there is no formula to do so. It is possible to find similar triangles

### Using Pythagorean Theorem to draw exact lengths.

Represent the following lengths on a square lattice. Show all your work. a. square root of 5 b. square root of 17 c. square root of 18 d. square root of 29