RandTrigTest.mws

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A Randomized Trigonometry Test

by Otto Wilke
otto_wilke@hotmail.com

Randomized tests inhibit cheating and reduce the number of student-teacher confrontations. The code below produces randomized trigonometry tests from a test bank of 35 problems.

To make the code below functional, it is necessary to download and execute the file trigtest.mws. Execution of that file will create a binary file named trigtest.m. The code below will open the trigtest.m file.

To generate a test without answers, set answers:=0: To generate the same version with answers, set answers:=1:
To scramble the arrangement of problems, set Permutation:= 1:
To have a description of the type of problem precede the problem, set Description:=1:

Because of the way the code is written, it is not possible to produce both scrambled and unscrambled editions of the same version. Version 1 scrambled will have different coefficients and answers than Version 1 unscrambled.

It might be wise to set the seed for the random number generator, _seed, to some secret function of the version number. That would prevent students who read this from generating the test with answers.

Enter desired problem numbers from the test bank of 35 problems into list1. The same problem number can be entered in the list more that once to create variants of the same problem. Problems 3, 23, 24, and 25 have no variants. Problem 27 has only four variants.

Because the test below contains all 35 problems and is not scrambled, the problem numbers are the same as the test bank numbers.

> with(Units):with(Units[Natural]):
read `trigtest.m`:with(combinat):
Version:=1:_seed:=Version:answers:=1:Permutation:=0:Description:=1:
printf("Randomized Trig Test\n");
list1:=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]:
if Permutation = 1 then
list1:=randperm(list1):
end if:
for j from 1 to nops(list1) do
printf("Problem% d, Version% d\n",j,Version);
s1:=``||op(j,list1):
if Description = 1 then
trigtest[`d`||s1]();end if:
trigtest[`p`||s1](answers);printf("\n");od:

Warning, the name Unit has been rebound

Warning, the assigned name polar now has a global binding

Warning, these protected names have been redefined and unprotected: *, +, -, /, <, <=, <>, =, Im, Re, ^, abs, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, argument, ceil, collect, combine, conjugate, convert, cos, cosh, cot, coth, csc, csch, csgn, diff, eval, evalc, evalr, exp, expand, factor, floor, frac, int, ln, log, log10, max, min, normal, root, round, sec, sech, shake, signum, simplify, sin, sinh, sqrt, surd, tan, tanh, trunc, type, verify

Warning, the protected name Chi has been redefined and unprotected

Randomized Trig Test

Problem 1, Version 1

Convert degrees to radians.

Convert 315 degrees to radians.

Problem 2, Version 1

Convert radians to degrees.

Convert the following from radians to degrees.

Problem 3, Version 1

Trig function definitions.

Given a right triangle with angles A, B, and C,

(C = 90 degrees), and with opposite sides a, b, and c,

draw the triangle, label the sides and angles, identify the right angle,

and give the six trig functions of A and of B in terms of a, b, and c.

Warning, the name changecoords has been redefined

Problem 4, Version 1

Exact trig functions of special angles in Quadrant I.

Give the exact values of the following.  Angle given in degrees.

Answer:

Problem 5, Version 1

Exact sin, cos, or tan of special angles.

Give the exact values of the following.  Angle given in degrees.

Answer:

Problem 6, Version 1

Exact sec, csc, or cot of special angles.

Give the exact values of the following.  Angle given in degrees.

Answer:

Problem 7, Version 1

Find trig function of quadrantal angle.

Give the exact values of the following.  Angle given in degrees.

Answer:

Problem 8, Version 1

Trig function given degrees and minutes.

What is the value of the cos of 15 degrees and 38 minutes?

Problem 9, Version 1

Trig function given angle in radians.

What is the value of the sin of  2.050 radians

Problem 10, Version 1

Trig function given decimal degrees.

What is the value of the sin of  83.43 degrees?

Problem 11, Version 1

Find angle in degrees given sin, cos, or tan.

What is the value of an acute angle, in degrees,

if its sin is  .8032?

Problem 12, Version 1

Find angle in degrees given sec, csc, or cot.

What is the value of an acute angle, in degrees,

if its sec is  2.559?

Problem 13, Version 1

Solving right triangles.

Given a triangle with angles A, B, C (C=90 degrees),

with corresponding opposite sides a, b, and c,

find the remaining sides and/or angles given the following:

Answer:

Problem 14, Version 1

Right triangle application.

A river with parallel banks flows from north to south.

Point T is on the west bank directly across from point S

on the east bank.  An engineer measures 160 feet from point S

to point R which is also on the east bank. Angle RST is 90 degrees.

Angle TRS is 58 degrees and 47 minutes.  How wide is the river?

Problem 15, Version 1

Second right triangle application.

Find the length of a guy wire that makes an angle

of 41 degrees and 8 minutes with the ground

if the wire is attached to a vertical tower  128.5 meters tall.

Problem 16, Version 1

Third right triangle application.

A hill makes an angle of  11.6 degrees with the horizontal.

From the base of the hill, the angle from horizontal to

the top of a tree on the hill is  23.8 degrees.

The distance along the slope from the base of the hill to

the base of the tree is 146 feet. Find the height of the tree.

Problem 17, Version 1

Find arc length.

In a circle of radius  39.5 inches, find the length of

arc subtended by a central angle of 93 degrees.

Problem 18, Version 1

Find linear velocity.

The angular velocity of a flywheel is 312 radians/min.

Find the linear velocity of a point which is  21.0 inches

from the center of the flywheel.  Give answer is inch/min and m/s.

Problem 19, Version 1

Rotary motion application.

A gear is driven by a chain that travels  2.13 m/s.

Find the radius of the gear is it makes 51 revolutions per minute.

Problem 20, Version 1

Find area of a sector of a circle.

Find the area of a sector of a circle whose central angle

is 204 degrees and whose radius is  4.25 inches.

Problem 21, Version 1

Use Heron's formula to find area of a triangle.

Jim plans to paint a triangular wall in his A-frame cabin.

Two sides measure 12 m each and the third side is 9 m.

How many cans of paint will he need if each can

covers  7.3 square meters?

Problem 22, Version 1

Area of triangle application.

A real estate agent wants to find the area of a triangular lot.

Two sides measure  86.0 m and  58.4 m. The angle between

them is  56.9 degrees.  What is the area of the lot?

Problem 23, Version 1

Plot sin(x) and cos(x) over one period.

Plot the sin(x) and the cos(x) over the

interval 0 to 360 degrees.  Label the abscissa in degrees

and in submultiples of Pi.

Problem 24, Version 1

Plot tan(x) and cot(x) over one period.

Plot the tan(x) and the cot(x) over one period.

Begin each at an asymptote.  Label the abscissa in degrees

and in submultiples of Pi.

Problem 25, Version 1

Plot sec(x) and csc(x) over one period.

Plot the sec(x) and the csc(x) over one period.

Begin each at an asymptote.  Label the abscissa in degrees

and in submultiples of Pi.

Problem 26, Version 1

Plot a function of sin(x) and give period, amplitude, and translations.

What are the vertical shift,the amplitude, the period, and the horizontal

shift of the following function.

Plot the function over one period only, beginning

where y is at the midpoint of its range.

Answer:

Problem 27, Version 1

Verify an identity.

Determine whether the following is an identity.

Answer:

Identity

Problem 28, Version 1

Divide complex numbers in polar form.

Divide and express answer in rectangular form (Angles given in degrees).

Answer:

Problem 29, Version 1

Raise a complex number to a power.

Evaluate and express answer in rectangular form.

Problem 30, Version 1

Find the roots of a complex number.

Find the cube roots of the following complex number.

Express answer in rectangular form.

Problem 31, Version 1

Solve a trigonometric equation.

Find all solutions of the following equation in the

    interval [0,360) degrees.

Answer:

Problem 32, Version 1

Solve oblique triangles.

Given a triangle with angles A, B, and C, in degrees, and

opposite sides a, b, and c, solve the triangle

and find the area of the triangle, given:

Answer:

Problem 33, Version 1

Ramp application.

A force of 318 lb. is required to pull a boat up a ramp

inclined at 18 degrees with the horizontal.  Neglecting friction,

how much does the boat weigh?

Problem 34, Version 1

Add forces.

Forces of  40.6 N and  48.2 N act on an object.  The angle

between the forces is  39.5 degrees.  Find the magnitude

of the resultant.

Answer:

Problem 35, Version 1

Airplane application.

A plane is headed on a bearing of 206 degrees with an

air speed of 220 miles per hour.  A wind from a direction

of 74 degrees is blowing at 34 mph.  Find the ground speed

and ground bearing of the plane.

Answer:

Because the test above contained all 35 problems and was not scrambled, the problem numbers are the same as the test bank numbers.

Below is a short test on oblique triangles to illustrate variants of the same problem.

> with(Units):with(Units[Natural]):
read `trigtest.m`:with(combinat):
Version:=4:_seed:=Version:answers:=0:Permutation:=0:Description:=0:
printf("Randomized Trig Test\n");
list1:=[32,32,32,32,32]:
if Permutation = 1 then
list1:=randperm(list1):
end if:
for j from 1 to nops(list1) do
printf("Problem% d, Version% d\n",j,Version);
s1:=``||op(j,list1):
if Description = 1 then
trigtest[`d`||s1]();end if:
trigtest[`p`||s1](answers);printf("\n");od:

Warning, the name Unit has been rebound

Warning, the name Unit has been rebound

Randomized Trig Test

Problem 1, Version 4

Given a triangle with angles A, B, and C, in degrees, and

opposite sides a, b, and c, solve the triangle

and find the area of the triangle, given:

Problem 2, Version 4

Given a triangle with angles A, B, and C, in degrees, and

opposite sides a, b, and c, solve the triangle

and find the area of the triangle, given:

Problem 3, Version 4

Given a triangle with angles A, B, and C, in degrees, and

opposite sides a, b, and c, solve the triangle

and find the area of the triangle, given:

Problem 4, Version 4

Given a triangle with angles A, B, and C, in degrees, and

opposite sides a, b, and c, solve the triangle

and find the area of the triangle, given:

Problem 5, Version 4

Given a triangle with angles A, B, and C, in degrees, and

opposite sides a, b, and c, solve the triangle

and find the area of the triangle, given:

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