Question

In: Computer Science

Write 2 MATLAB functions. One called exptrig which takes a vector of arbitrary length, x, containing...

Write 2 MATLAB functions. One called exptrig which takes a vector of arbitrary length, x, containing any real numbers, and computes the mathematical function

f(x) = 3e^(-x)(cos^2(5x) - sin^2(5x)). The other one will be called trigsum, which takes a vector arbitrary length, x, containing any real numbers, and computes the mathematical function g(x)= ((sin(10x) + cos(10x))/ 2) + 3. Both functions will be computed at each of the values of x, and internally will output these values into a vector, y, of the same dimensions as x.

a) input x1=3 and assign outputs to y1 and z1

b) input a vector x^2, which is the transpose of linspace(-2*pi,2*pi,100), and assign outputs to y2 and z2

c) input a vector x3 = -10:10, and assign outputs y3 and z3

d) input x4= -300, and assign outputs y4 and z4

%sets up a random input vector of integers, of random length

len = randi([1 10],1,1);

x5 = randi([-10 10], 1, len);

y5 = exptrig(x5);

z5 = trigsum(x5)

Expert Solution

First funtion.

function fx=exptrig(x)
    
    fx=3.*(exp(-1.*x)).*((cos(5*x)).^2 - (sin(5*x)).^2);
end

Second function

function gx= trigsum(x)
    
    gx= ((sin(10*x) + cos(10*x))./ 2) + 3;
end

Test program

% quesion 1
x1=3
y1=exptrig(x1)
z1=trigsum(x1)

%question2 
x2=linspace(-2*pi,2*pi,100);
x2=(x2)'
y2=exptrig(x2)
z2=trigsum(x2)

% question 3
x3=-10:1:10

y3=exptrig(x3)
z3=trigsum(x3)

% question 4

x4=-300

y4=exptrig(x4)
z4=trigsum(x4)

% question 5

len = randi([1 10],1,1);
x5 = randi([-10 10], 1, len)
y5 = exptrig(x5)
z5 = trigsum(x5)

Simulated result is shown below.

>> test

x1 =

     3


y1 =

    0.0230


z1 =

    2.5831


x2 =

   -6.2832
   -6.1563
   -6.0293
   -5.9024
   -5.7755
   -5.6485
   -5.5216
   -5.3947
   -5.2677
   -5.1408
   -5.0139
   -4.8869
   -4.7600
   -4.6331
   -4.5061
   -4.3792
   -4.2523
   -4.1253
   -3.9984
   -3.8715
   -3.7445
   -3.6176
   -3.4907
   -3.3637
   -3.2368
   -3.1099
   -2.9829
   -2.8560
   -2.7291
   -2.6021
   -2.4752
   -2.3483
   -2.2213
   -2.0944
   -1.9675
   -1.8405
   -1.7136
   -1.5867
   -1.4597
   -1.3328
   -1.2059
   -1.0789
   -0.9520
   -0.8251
   -0.6981
   -0.5712
   -0.4443
   -0.3173
   -0.1904
   -0.0635
    0.0635
    0.1904
    0.3173
    0.4443
    0.5712
    0.6981
    0.8251
    0.9520
    1.0789
    1.2059
    1.3328
    1.4597
    1.5867
    1.7136
    1.8405
    1.9675
    2.0944
    2.2213
    2.3483
    2.4752
    2.6021
    2.7291
    2.8560
    2.9829
    3.1099
    3.2368
    3.3637
    3.4907
    3.6176
    3.7445
    3.8715
    3.9984
    4.1253
    4.2523
    4.3792
    4.5061
    4.6331
    4.7600
    4.8869
    5.0139
    5.1408
    5.2677
    5.3947
    5.5216
    5.6485
    5.7755
    5.9024
    6.0293
    6.1563
    6.2832


y2 =

   1.0e+03 *

    1.6065
    0.4201
   -1.0265
   -0.8629
    0.3451
    0.8499
    0.1768
   -0.5669
   -0.4337
    0.2129
    0.4478
    0.0690
   -0.3113
   -0.2164
    0.1283
    0.2350
    0.0234
   -0.1701
   -0.1071
    0.0759
    0.1228
    0.0053
   -0.0925
   -0.0525
    0.0443
    0.0639
   -0.0009
   -0.0501
   -0.0255
    0.0255
    0.0331
   -0.0025
   -0.0270
   -0.0122
    0.0146
    0.0171
   -0.0024
   -0.0145
   -0.0057
    0.0082
    0.0088
   -0.0018
   -0.0077
   -0.0026
    0.0046
    0.0045
   -0.0012
   -0.0041
   -0.0012
    0.0026
    0.0023
   -0.0008
   -0.0022
   -0.0005
    0.0014
    0.0011
   -0.0005
   -0.0012
   -0.0002
    0.0008
    0.0006
   -0.0003
   -0.0006
   -0.0001
    0.0004
    0.0003
   -0.0002
   -0.0003
   -0.0000
    0.0002
    0.0001
   -0.0001
   -0.0002
   -0.0000
    0.0001
    0.0001
   -0.0001
   -0.0001
    0.0000
    0.0001
    0.0000
   -0.0000
   -0.0000
    0.0000
    0.0000
    0.0000
   -0.0000
   -0.0000
    0.0000
    0.0000
    0.0000
   -0.0000
   -0.0000
    0.0000
    0.0000
    0.0000
   -0.0000
   -0.0000
    0.0000
    0.0000


z2 =

    3.5000
    3.6259
    2.8717
    2.2979
    2.7114
    3.5307
    3.6038
    2.8278
    2.2940
    2.7529
    3.5593
    3.5792
    2.7847
    2.2929
    2.7954
    3.5856
    3.5523
    2.7424
    2.2947
    2.8388
    3.6095
    3.5232
    2.7012
    2.2993
    2.8827
    3.6311
    3.4920
    2.6611
    2.3068
    2.9272
    3.6500
    3.4588
    2.6224
    2.3170
    2.9720
    3.6664
    3.4238
    2.5853
    2.3300
    3.0168
    3.6800
    3.3870
    2.5498
    2.3457
    3.0616
    3.6909
    3.3487
    2.5161
    2.3640
    3.1062
    3.6991
    3.3090
    2.4844
    2.3848
    3.1503
    3.7044
    3.2680
    2.4547
    2.4082
    3.1938
    3.7069
    3.2260
    2.4273
    2.4339
    3.2366
    3.7066
    3.1830
    2.4021
    2.4619
    3.2784
    3.7033
    3.1393
    2.3794
    2.4921
    3.3190
    3.6973
    3.0951
    2.3591
    2.5244
    3.3584
    3.6885
    3.0504
    2.3415
    2.5585
    3.3963
    3.6769
    3.0056
    2.3265
    2.5944
    3.4327
    3.6625
    2.9608
    2.3142
    2.6320
    3.4673
    3.6455
    2.9161
    2.3046
    2.6710
    3.5000


x3 =

   -10    -9    -8    -7    -6    -5    -4    -3    -2    -1     0     1     2     3     4     5     6     7     8     9    10


y3 =

   1.0e+04 *

  Columns 1 through 20

    5.6982   -1.0892   -0.0987    0.2084   -0.1153    0.0430   -0.0109    0.0009    0.0009   -0.0007    0.0003   -0.0001    0.0000    0.0000   -0.0000    0.0000   -0.0000    0.0000   -0.0000   -0.0000

  Column 21

    0.0000


z3 =

  Columns 1 through 20

    3.6843    2.3290    3.4418    2.9297    2.6762    3.6137    2.2940    3.5711    2.7476    2.8525    3.5000    2.3085    3.6605    2.5831    3.0391    3.3513    2.3714    3.7036    2.4479    3.2230

  Column 21

    3.1780


x4 =

  -300


y4 =

 -5.6856e+130


z4 =

    2.4026


x5 =

    10    10


y5 =

   1.0e-03 *

    0.1174    0.1174


z5 =

    3.1780    3.1780

Hope you got the answer. If you still have any doubts regarding this, please try to comment , i will help you.

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