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Q1 solve the following equation for the angle between 0 - 360 (6 Marks) (a) 6sin...
1) Allow f(x) = x3, and g(x) = 2x. Determine f(g(1)). 2) Enter the formula for...
1) Allow f(x) = x3, and g(x) = 2x. Determine f(g(1)). 2) Enter the formula for a sine function with an amplitude of 5, a period of 90 degrees, a shift of 45 degrees to the right and 3 units upwards. Determine the exact value of the expression sin (v) + cos (v) given that tan (v) = 7/3. 3) Solve the equations in the range 180≤x≤360 degrees. Answer with one decimal. a) tan (x) = 3.2 (I would like...
Question 2 (1 point) For the following equation,find all solutions exactly on the interval 0 0<360°...
Question 2 (1 point) For the following equation,find all solutions exactly on the interval 0 0<360° 6sin(0) 3V2 Enter your answers in degrees without units or other marks; place the smaller angle in blank #1 and the larger angle in blank #2. Blank # 1 Blank # 2 Question 3 (1 point) Determine the smallest positive angle that satisfies the following equation. 3 sec(a) 8 Enter your answer in radians, using pi to denote π
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform...
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform 10<tsI g(t) = le-3, +1 , 1<t 2 .22 Q2 Use Laplace transform to solve the following initial value problem: yty(o)-0 and y (0)-2 A function f(x) is periodic of period 2π and is defined by Q3 Sketch the graph of f(x) from x-2t to2 and prove that 2sinh π11 f(x)- Q4 Consider the function f(x)=2x, 0<x<1 Find the a Fourier cosine series b)...
15. The point (-6,-8) is on the terminal arm of LA-which is the correct value of...
15. The point (-6,-8) is on the terminal arm of LA-which is the correct value of csc A? a. 4 ー c. 3 16. Determine two angles between 0° and 360° that have a cosecant of -2. 17. Determine two angles between 0 and 360° that have a secant of 2. 18. Determine two angles between 0° and 360° that have a cotangent of 3. 19. A periodic function. (x) has a period of 12 and/(14)--5. What is the next...
11.1 and 11.2 Fourier Series Q1 Find the Fourier series of the given function f(x), which is assu...
11.1 and 11.2 Fourier Series Q1 Find the Fourier series of the given function f(x), which is assumed to have the period 2π. Show the details of your work. Sketch or graph the partial sums up to that including cos 5x and sin 5x. Note: Plot the partial sum using MATLAB. Hint: Make use of your knowledge of the line equation to find f(x) from the given graph. -π 0
11.1 and 11.2 Fourier Series Q1 Find the Fourier series...
1 2 NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the...
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NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...
6. For f(x) = 2 + tan for-360° SXS 360°. (a) For what values are there...
6. For f(x) = 2 + tan for-360° SXS 360°. (a) For what values are there asymptotes? (b) Write down (i) the period of the function; (ii) the value off (90°). (e) Solve f (x) = 0 for -360° SXS 360°. 4. Let (c) - cos (2x + 2), 0 S IS A. Sketch the curve of y=f(x) on the grid below. os | 15 1 25 35 The following graph shows the depth of water, y metres, at a...
One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to b...
One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to be observed in this laboratory assignment are shown below. In all the examples A represents the amplitude of the signal and may be given as the measurement from 0 to the peak value A, Apk or can be given as the measurement between A and -A which defines a peak-to-peak...
4. Let f(x) = 6-2x, 0
4. Let f(x) = 6-2x, 0<x 2 (a) Expand f(x) into a periodic function of period 2, ie. construct the function F(x), such that F(x)-f (x), 0xS 2, and Fx) F(x+2) for all real numbers x. (This process is called the "full-range expansion" of f(x) into a Fourier series.) Find the Fourier series of Fr). Then sketch 3 periods of Fx). (b) Expand fx) into a cosine series of period 4. Find the Fourier series and sketch 3 periods (c)...
l etisalat 5:45 PM 슐 moodle.ud.ac.ae 11.1 and 11.2 Fourier Series Q1 Find the Fourier series...
l etisalat 5:45 PM 슐 moodle.ud.ac.ae 11.1 and 11.2 Fourier Series Q1 Find the Fourier series of the given function f(x), which is assumed to have the period 2π. Show the details of your work. Sketch or graph the partial sums up to that including cos 5x and sin 5x Note: Plot the partial sum using MATLAB Hint: Make use of your knowledge of the line equation to find f) from the given graph. 2 Find the Fourier integral representation...
Question 2 (1 point) For the following equation,find all solutions exactly on the interval 0 0<360° 6sin(0) 3V2 Enter your answers in degrees without units or other marks; place the smaller angle in blank #1 and the larger angle in blank #2. Blank # 1 Blank # 2 Question 3 (1 point) Determine the smallest positive angle that satisfies the following equation. 3 sec(a) 8 Enter your answer in radians, using pi to denote π
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform 10<tsI g(t) = le-3, +1 , 1<t 2 .22 Q2 Use Laplace transform to solve the following initial value problem: yty(o)-0 and y (0)-2 A function f(x) is periodic of period 2π and is defined by Q3 Sketch the graph of f(x) from x-2t to2 and prove that 2sinh π11 f(x)- Q4 Consider the function f(x)=2x, 0<x<1 Find the a Fourier cosine series b)...
15. The point (-6,-8) is on the terminal arm of LA-which is the correct value of csc A? a. 4 ー c. 3 16. Determine two angles between 0° and 360° that have a cosecant of -2. 17. Determine two angles between 0 and 360° that have a secant of 2. 18. Determine two angles between 0° and 360° that have a cotangent of 3. 19. A periodic function. (x) has a period of 12 and/(14)--5. What is the next...
11.1 and 11.2 Fourier Series Q1 Find the Fourier series of the given function f(x), which is assumed to have the period 2π. Show the details of your work. Sketch or graph the partial sums up to that including cos 5x and sin 5x. Note: Plot the partial sum using MATLAB. Hint: Make use of your knowledge of the line equation to find f(x) from the given graph. -π 0
11.1 and 11.2 Fourier Series Q1 Find the Fourier series...
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NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...
6. For f(x) = 2 + tan for-360° SXS 360°. (a) For what values are there asymptotes? (b) Write down (i) the period of the function; (ii) the value off (90°). (e) Solve f (x) = 0 for -360° SXS 360°. 4. Let (c) - cos (2x + 2), 0 S IS A. Sketch the curve of y=f(x) on the grid below. os | 15 1 25 35 The following graph shows the depth of water, y metres, at a...
One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to be observed in this laboratory assignment are shown below. In all the examples A represents the amplitude of the signal and may be given as the measurement from 0 to the peak value A, Apk or can be given as the measurement between A and -A which defines a peak-to-peak...
4. Let f(x) = 6-2x, 0<x 2 (a) Expand f(x) into a periodic function of period 2, ie. construct the function F(x), such that F(x)-f (x), 0xS 2, and Fx) F(x+2) for all real numbers x. (This process is called the "full-range expansion" of f(x) into a Fourier series.) Find the Fourier series of Fr). Then sketch 3 periods of Fx). (b) Expand fx) into a cosine series of period 4. Find the Fourier series and sketch 3 periods (c)...
l etisalat 5:45 PM 슐 moodle.ud.ac.ae 11.1 and 11.2 Fourier Series Q1 Find the Fourier series of the given function f(x), which is assumed to have the period 2π. Show the details of your work. Sketch or graph the partial sums up to that including cos 5x and sin 5x Note: Plot the partial sum using MATLAB Hint: Make use of your knowledge of the line equation to find f) from the given graph. 2 Find the Fourier integral representation...
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