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# Trigonometry

### 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

### 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

### 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

### 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

### 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.

### 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)

### 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

### 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

### 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

### Circumscribable Quadrilateral and Finding Lengths

In the attached figure, the quadrilateral ABCD has the following lengths of sides and diagonals: DC=7, CB=8, BA=13, AD=13, AC=15, and BD=13. 1. Verify that quadrilateral ABCD is circumscribable 2. Find the remaining lengths of DE, BE, AE, and CE. Although it appears there is a right angle, it is not labeled as though it

### Trigonometric Points in terms of Radians : Transformations

In terms of radians and X, what would be the specifications of the anlges for trigonometric points which result from the following transformations of the trigonometric point P(X)? (Work these out on a diagram of the unit circle) 1) A reflection y = x followed by a rotation through pi 2) A reflection in y = -x 3) A refle

### Crystallographic Group: Relationship to A5 Group

Can the group A5 be a subgroup of the rotation group in a three dimentional crystallographic group?

### Formula for a sine curve given the amplitude and either the period, frequency or angular frequency.

(i) In london in 2002, the maximum number of daylight hours in a day was 16.63, and this was recorded in week 25.The minimum number of daylight hours in a day was 7.82, and this was recorded in week 51. The number of daylight hours in a day can be modelled approximately by using a sine function. Use the information given abo

### Pythagoras Theorem, Cosine and Sine Formulas

1) A herring gull was ringed at Llyn Trawsfynydd Gwynedd (grid reference SH 700360) and was retapped near Criccieth, Gwynedd ( grid reference SH 500380). The ringing report states the Distance as 20km and the Direction as 276 degrees. (a) Use the grid references and trigonometry to check that the map bearing of Criccieth from

### Writing a trigonometric function for a bouncing ball.

Write a trigonometric function for a ball dropped from a distance of 5ft from the floor. Let the x-axis represent the time after the ball was dropped and the y axis represent the height in feet. Address these issues: 1. Explain the process you used to find the function. Include all math steps. Why did you select this particular

### Further trigonometry and four point method

How do you understand further trigonometry and four-point method?

### Trigonometric Functions and Trigonometric Identities

I need to know the trigonometric functions and trigonometric identities.

### Proving trigonometry identities.

Prove this identity. (cot^2 X) - (cos^2 X) = (cot^2 X)(cos^2 X)

### Angle of Depression - Trigonometry

The foot, F, of a hill and the base B, of a vertical tower TB, 27 metres tall, are on the same horizontal plane. From the top, T, of the tower, the angle of depression of F is 32.7 degrees. P is a point on the hill 27.5 metres away from F along the line of greatest slope. T, B, F and P all lie in the same vertical plane. The ang