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Trigonometry

Trigonometry and Geometry Word Problems

3) A building 210 feet tall casts a 90 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 4 feet above ground level.) A) 66.40° B) 64.09° C

How far is the train from the crossing?

A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?

Trigonometry for Oblique Triangles

1.-On the shore of the lake,a surveyor measured a straigth line of 30 meters between point A and B.what is the shortest distance between the point C on the island and the point A on the shore if angle C A B = 23degrees and 50 minutes and angle C B A =67 degrees and 28 minutes. 2.-Find the angle B in an oblique triangle in whi

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

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

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.

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

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?

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

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

Trigonometry Application Word Problems - Fire Center

Researchers at the National Interagency Fire center in Boise , Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States . In an effort to dispatch firefighters for containment , scientists and meteologists attempts to forecast

Trigonometry Application Word Problems

A recent land survey was conducted on a vacant lot where a commercial building is to be erected . The plans for the future building construction call for a building having a roof supported by two sets of beams. The beams in the front are 8 feet high and the back beams

Trigonometry Applications to Word 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. Complete the following problems: 1. A lobster boat is situated due west of a lighthouse. A barge is 12 km south of the lobster boat .

Find the exact value of the sine, cosine, and tangent of angles

1. Find the exact value of the sine, cosine, and tangent of the angle. 11pie/12 2. Find all solutions of the equation in the interval [0, 2pie). Sin(x-5pie/6)-sin(x+ 5pie/6) =1 3. Find the exact value of sin2x using the double angle formula. Please help explain the use of the double angle formula. Sin x=1/7,

Finding the height of the wall.

Elena likes to climb a vertical rock wall at an amusement park. From a point that is 10M from the base of the wall, the angle of the elevation of the top of the wall is 72 degree. What is the height of the wall, to the nearrest metre?