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Trigonometry

Trigonometric Equations and Identities

1. Solve each equation for the domain interval 0 less than or equal to x less than or equal to 2pie. Round the answers to the nearest hundredth of a radian, if necessary. a) 2cossquaredx+cosx=0 b) tansquaredx-1=0 c) 6sinsquaredx+sinx-1=0 2. Simplify each trigonometric expression. a) sinx (Suppo

Trigonometry and Pythagorean (Pythagorus) Theorem Problems

1.-In a right triangle with the hypotenuse c = 10 and the angle A =50 degrees ,what is the value of side b ? 2.- If in a right triangle the angle A = 40 degrees ,and the side a = 5,what is the value of side b ? 3.-If in a right triangle the hypotenuse c =12 and the side b = 5, what is the value of the angle A ? use natu

Trig

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

Trigonometry Word Problems (4 Problems)

You have been contacting cartographers and land surveyors to explore how they utilize graphs of functions in their work, and have learned that they create formulas to calculate size and mass. 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 l

Trigonometry Word Problems

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?

Trigonometric Equations and Identities and Tire Wear Problem

You interviewed an employee of 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 2003, a safety group asked the U

Trigonometric Equations and Identities

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? Explai

Word problem on braking distance

Trigonometry: D = 1.05 (V1^2 - V2^2)/64.4(K1 + K2 + sin θ) K1 is a constant determined by the efficiency of the brakes and tires, K2 is a constant determined by the rolling resistance of the automobile, and θ is the grade of the highway. a. Compute the number of feet required to slow a car from 55 mph to 30 m

Pythagorean theorem

A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, , where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides' measurements are 6 feet and 8 feet.

Hypotenuse from Pythagorean Theorem

A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, , where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides' measurements are 6 feet and 8 feet.

Solving Equations, Length of a Cube and Pythagorean Theorem

1. a. square root of x-2 = 1 show work b. square root of x cubed = 27 show work c. 3 x the square root of x squared = 9 show work 2. Is the square root of x squared = x an identity (true for all non values of x?) Explain answer 3. For the equation x - 2 times square root of x on the same gr

Applications of Sines : Trigonometry Word Problems

A ranger in fire tower A spots a fire at a direction of 295 degrees. A ranger in fire tower B, located 45 miles at a direction of 45 degrees from A, spots the same fire at direction of 255 degrees. How far from tower Ais the fire? From tower B?

Matlab Spectra Plot : Convolution with Low-Pass Filter

Lpf = ones(1,10); y=abs(fft([lpf zeros(1,246)])); Create a signal consisting of a 500 and 1000Hz cosine sampled t 10kHz. fs= 10e3; t =(0:1:0.02*fs); f1=500; f2=1000; s=cos(2*pi*t*f1/fs)+cos(2*pi*t*f2/fs); Plot the convolution of the signal with lpf, from the command filtered=conv(s,lpf) **Plot the magnitude of th

10 Trigonometry Problems

1. Find B to the nearest degree in triangle ABC given A = 34 degrees, b=7.0 and a = 11. 2. How do you convert from degrees to radians. Explain and provide an example with 283 degrees. 3. The hypotenuse of a 30-60-90 triangle is 10. Find the perimeter 4. Given C= 61 degrees, a=55, and b= 29, find the area of triang

Problems in calculus and trigonometry

Do the following problems: (1) Find the value of twice the integral of the function u^(-1) + 3*[u^(-2)] over the interval [-3, -1]. (2) Show that cot(pi/3) = 1/[sqrt(3)], where "sqrt" stands for "square root." (3) Obtain the Maclaurin series for the function f(x) = sin x. (4) Obtain the Maclaurin series for the funct

Values of tangent (tan A) of an angle

Consider the graph of y = tan x (see attached). (a) How does it show that the tangent of 90 degrees is undefined? (b) What are other undefined x values? (c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)? (d) How does the graph show this?

The Application of Trigonometry

Please view the attached file to see the diagram which accompanies this question. 1. Find the length L from point A to the top of the pole. 2. Lookout station A is 15 km west of station B. The bearing from A to a fire directly south of B is S 37°50' E. How far is the fire from B? 3. The wheels of a car have a 24-in. diam

Trigonometry

A regular octagon is inscribed in a circle of radius 15.8 cm. Find the perimeter of the octagon.

Geometry Applications

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of

Pythagorean (Pythagorus) Theorem Question

A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides' measurements are 3 feet and 4 feet.

Consider the graph of y = tan x.

1. Consider the graph of y = tan x. (a) How does it show that the tangent of 90 degrees is undefined? (b) What are other undefined x values? (c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)? (d) How does the graph show this? 2. A nautical mile depends on l

Polar Equations : Identify the curves by finding a cartesian

Solve step by step showing all work and give answer. I) Identify the curves, (16-20) by finding a cartesian equation for the curve. You know, using x=rcostheta, y = rsintheta, etc..... 16) rcos(theta)=1 18) r=2sin(theta) + 2cos(theta) 20) r=tan(theta)sec(theta) II)Find a polar equation for the curve represented b

Applications of Trigonometry : Latitude, Longitude and Nautical Miles

2. A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos 2P, where P is the latitude in degrees. (a) Using the Cybrary and other course resources, find the exact latitude (to 4 decimal places) of where you live, used to live, work, or used to

Find the equation of a tangent given parametric equations

1.) Find and equation of the tangent to the curve at the point corresponding to the given value of the parameter x= cos t + sin 2t, y= sin t + cos 2t (t=0) 2.) Find dy/dx and d^2/dx^2 for which values of t is the curve concave upward x= t + ln t, y = 1 - ln t

Using Trigonometry to Find Lengths

1. Find the length L from point A to the top of the pole. See attachment for diagram. 2. Lookout station A is 15 km west of station B. The bearing from A to a fire directly south of B is S 37°50' E. How far is the fire from B? 3. The wheels of a car have a 24-in. diameter. When the car is being driven so that the wheels

Travel in kilometers

Suppose you travel north for 65 kilometers then travel east 75 kilometers. How far are you from your starting point? Please show your work to help me understand how to do this.