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
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
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?
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
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
See attached please.
(See attached file for full problem description)
(See attached file for full problem description)
Use an identity to write each expression with a single trigonometric function. See attached file.
Write each expression as a sum or difference of trigonometric functions (See attached file for full problem description) sin(4x)* sin(5x).
Used identities to find each exact value (See attached file for full problem description)
Simplify to a constant, single function or a power of a function. Use the fundamental identities to simplify. (See attached file for full problem description)
Perform each indicated operation and simplify the result. See attached file for full problem description.
Amplitude, period and shift of function. See attached file for full problem description.
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
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See attached file for full problem description. Solve for the tan and cot.
(See attached file for full problem description) Let be a complex number, and assume the identity where are positive real numbers. By expanding the tan function, show that if , then is approximately equal to for some integer
1) Express (cosx)^n in terms of sums of coskx 2) Express (sinx)^n in terms of sums of coskx or sinkx 3) Express cosnx in terms of sums of (cosx)^k 4) Express sinnx in terms of sums of (sinx)^k 5) Derive exact trigonometric identities for sin(k*pi) for k being: 1/12, 1/10,1/8,1/6,1/5,1/4,3/10,1/3,3/8,2/5,5/12
See the attached file for full problem description. 1. What was the most interesting thing that you learned in studying plane trigonometrfy? Tell briefly why you selected it as your choice. 2. Following the instructions in Art. 4, draw the portion of the graph of y = cos x from 0 degrees to 360 degrees. Be sure to show a t
(See attached file for full problem description) Write equivalent equations in the form of inverse functions for.... Verify the identity....
Manipulate trigonometric expressions, sketch graphs of trigonometric functions and solve equations. Find the general solution of the following trigonometric equations: 1. a) cosθcos(pi/6)+sinθsin(pi/6) =0.25 b) 2sin^2 x - 5cosx+ 1 = 0 2. Prove: cos(θ+ pi/4) - sin(θ + pi/4) = 2cos(θ+ pi/4)
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.
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.
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
Verify the following identities: a. cos x (tan^2 x + 1) = sec x b. 1 _________ = 1 tan x csc x c. (sin^2 x - sin^4 x)cos x = cos^3 x sin ^2 x
A boat leaves a port and sails 10 miles at a bearing of S 15° E. Another boat leaves the same port and sails 15 miles at a bearing of S 30° W. How far apart are the two boats at this point?
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?
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
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