menuicon

MATH1111 Quizzes

Differentiating Trigonometric Quiz
Web resources available Questions

This quiz tests the work covered in Lecture 16 and corresponds to Section 3.5 of the textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al.).

There are more web quizzes at Wiley, select Section 5.

Section 3.7 of The Mathematics Learning Centre’s booklet on differentiation Introduction to Differential Calculus covers differentiating trigonometric functions.

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/derivative/trig2.html gives another explanation of the derivative of the basic trigonometric functions.

There is an applet at http://www.ies.co.jp/math/java/calc/sin_diff/sin_diff.html which graphs the derivatives by looking at the tangent to the curve.

You might want to go back to http://www.math.ucdavis.edu/ kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html or http://archives.math.utk.edu/visual.calculus/2/chain_ rule.2/ and try the trigonometrical problems if you haven’t already.

Which of the following statements are correct? (Zero or more options can be correct)
a)
If f(x) = sin2x then f(x) = 2cos2x.
b)
If f(x) = sin3x then f(x) = 3cos3x.
c)
If f(x) = 2cosx then f(x) = sin2x.
d)
If f(x) = 3cosx then f(x) = 3sinx.
e)
If f(x) = 2tanx then f(x) = sec22x.

There is at least one mistake.
For example, choice (a) should be True.
There is at least one mistake.
For example, choice (b) should be False.
If f(x) = sin3x then f(x) = 3cos3x.
There is at least one mistake.
For example, choice (c) should be False.
If f(x) = 2cosx then f(x) = 2sinx.
There is at least one mistake.
For example, choice (d) should be True.
There is at least one mistake.
For example, choice (e) should be False.
If f(x) = 2tanx then f(x) = 2sec2x.
Correct!
  1. True
  2. False If f(x) = sin3x then f(x) = 3cos3x.
  3. False If f(x) = 2cosx then f(x) = 2sinx.
  4. True
  5. False If f(x) = 2tanx then f(x) = 2sec2x.
Which of the following is the derivative of  f(x) = cos(x2 + 3x)? Exactly one option must be correct)
a)
f(x) = sin(2x + 3)
b)
f(x) = sin(2x + 3)
c)
f(x) = (2x + 3)sin(x2 + 3x)
d)
f(x) = (2x + 3)sin(x2 + 3x)

Choice (a) is incorrect
Try again, you have not applied the chain rule correctly.
Choice (b) is incorrect
Try again, you have not applied the chain rule correctly.
Choice (c) is correct!
f(x) = (2x + 3) ×sin(x2 + 3x) = (2x + 3)sin(x2 + 3x)
Choice (d) is incorrect
Try again, watch the sign.
Which of the following is the derivative of  x = 2sin3t + cos2t? Exactly one option must be correct)
a)
dx dt = 6cos3t 2sintcost
b)
dx dt = 6cos3t 2cost
c)
dx dt = 6cos3tcos2t 2sintcostsin3t
d)
dx dt = 6cos3tcos2t 2costsin3t

Choice (a) is correct!
dx dt = 2 × 3cost + 2cost ×sint = 6cos3t 2sintcost
Choice (b) is incorrect
Try again, you have not used the chain rule correctly for the second term.
Choice (c) is incorrect
Try again, you have successfully found the derivative of  x = 2sin3t × cos2t.
Choice (d) is incorrect
Try again, you have seem to be trying to find the derivative of  x = 2sin3t × cos2t.
Which of the following is the derivative of  h(s) = tan3s + s3 + 3sins cos4s ? Exactly one option must be correct)
a)
h(s) = sec23s + (3s2 + 3coss)cos4s (s3 + 3sins)4sin4s cos24s
b)
h(s) = sec23s + (3s2 + 3coss)cos4s + (s3 + 3sins)4sin4s cos24s
c)
h(s) = 3sec23s + (3s2 + 3coss)cos4s (s3 + 3sins)4sin4s cos24s
d)
None of the above.

Choice (a) is incorrect
Try again, you have not differentiated the first term correctly, you may have a sign problem as well.
Choice (b) is incorrect
Try again, you have not differentiated the first term correctly.
Choice (c) is incorrect
Try again, you have not differentiated the second term correctly.
Choice (d) is correct!
h(s) = 3sec23s + (3s2 + 3coss)cos4s + (s3 + 3sins)4sin4s cos24s