# The Trigonometric Function Quiz

Question

## Web resources available

This quiz tests the work covered in Lecture 4 and corresponds to Section 1.5 of the textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al.).
There are further web quizzes at Wiley. Choose section 5 from this page.

Be aware that it doesn’t seem to accept the written answers so you will have to check whether your answers are correct when they print the correct answer. The answer to question 12 was incorrect on 31/10/05

There are some questions in the quizzes for MATH1011 that may be appropriate - omit questions 1 and 2 from http://www.maths.usyd.edu.au/u/UG/JM/MATH1011/Quizzes/quiz1.html but the other 8 questions are useful.

The Mathematics Learning Centre has a booklet on Introduction to Trigonometric Functions and tutors who can help you with the concepts.

There are some nice graphics of the sine function with different periods at http://www.ies.co.jp/math/products/trig/applets/graphSinAX/graphSinAX.html and at http://www.ies.co.jp/math/products/trig/applets/ABCsinX/ABCsinX.html. They look at the graphs in terms of angles instead of radians.

You can run applets from http://www.univie.ac.at/future.media/moe/galerie/fun2/fun2.html$♯$sincostan. Graphs of elementary trig functions allow you to see the graphs of sine, cosine and tangent and their relationship to travelling around a circle. Recognize functions and graphs are useful to test your understanding. The function plotter allows you to plot any function, make sure you read ‘Description’ to see how to enter functions.

## Question 1

Given that $sin\frac{\pi }{7}=0.434$ which of the following gives the value of $cos\frac{\pi }{7}$ correct to 3 decimal places?
Please do not use the trig functions on your calculator to answer this question.
 a) 0.812 b) 0.143 c) 0.901 d) 0.566

Not correct. Choice (a) is false.
Try again, you may not have used your calculator correctly.
You need to put $1-0.43{4}^{2}$ in brackets when you use the square root key.
Not correct. Choice (b) is false.
Try again, you may not have used your calculator correctly.
You must change your calculator to radians and use brackets carefully.
$cos\frac{\pi }{7}=\sqrt{1-sin{\frac{\pi }{7}}^{2}}=\sqrt{1-0.43{4}^{2}}=0.9009=0.901\phantom{\rule{0.3em}{0ex}}.$
Not correct. Choice (d) is false.
Try again, you need to find $\sqrt{1-0.43{4}^{2}}\phantom{\rule{0.3em}{0ex}}.$

## Question 2

Consider the four graphs below and match the graphs with the functions.
a)
 ${f}_{1}^{}\left(t\right)$ = $2sint$ ${f}_{2}^{}\left(t\right)$ = $2+sint$ ${f}_{3}^{}\left(t\right)$ = $sin\left(t+\frac{\pi }{2}\right)$ ${f}_{4}^{}\left(t\right)$ = $sin2t$
b)
 ${f}_{1}^{}\left(t\right)$ = $2+sint$ ${f}_{2}^{}\left(t\right)$ = $2sint$ ${f}_{3}^{}\left(t\right)$ = $sin\left(t+\frac{\pi }{2}\right)$ ${f}_{4}^{}\left(t\right)$ = $sin2t$
c)
 ${f}_{1}^{}\left(t\right)$ = $sin2t$ ${f}_{2}^{}\left(t\right)$ = $2sint$ ${f}_{3}^{}\left(t\right)$ = $sin\left(t+\frac{\pi }{2}\right)$ ${f}_{4}^{}\left(t\right)$ = $2+sint$
d)
 ${f}_{1}^{}\left(t\right)$ = $2+sint$ ${f}_{2}^{}\left(t\right)$ = $2sint$ ${f}_{3}^{}\left(t\right)$ = $sin2t$ ${f}_{4}^{}\left(t\right)$ = $sin\left(t+\frac{\pi }{2}\right)$

Not correct. Choice (a) is false.
Try again, you have confused the amplitude and the vertical translation.
Not correct. Choice (c) is false.
Try again, you have confused the change in period and the vertical translation.
Not correct. Choice (d) is false.
Try again, you have confused the change in period with the horizontal translation.

## Question 3

Consider the 2 graphs below
Which of the following statements is correct?
a)
 $f\left(x\right)$ = $cos\left(x-\frac{\pi }{2}\right)$ $g\left(x\right)$ = $cos\left(x+\frac{\pi }{2}\right)$
b)
 $f\left(x\right)$ = $cos\left(x+\frac{\pi }{2}\right)$ $g\left(x\right)$ = $cos\left(x-\frac{\pi }{2}\right)$

We translate to the right by subtracting from the argument and
we translate to the left by adding to the argument.
Not correct. Choice (b) is false.
Try again, we translate to the right by subtracting from the argument and
we translate to the left by adding to the argument.

## Question 4

Which of the following graphs would represent the vertical distance from the origin of a particle travelling 3 times around a circle, starting from the $x$-axis?
 a) b) c) d) e) There is not enough information to answer the question.

Not correct. Choice (a) is false.
Try again, this represents the horizontal distance of the particle from the origin.
Not correct. Choice (b) is false.
Try again, the particle hasn’t travelled far enough and it represents the horizontal distance of the particle from the origin.
Not correct. Choice (c) is false.
Try again, the particle hasn’t travelled far enough.
The particle has travelled $6\pi$ radians so it has gone around the circle 3 times and it starts with zero vertical distance so this is the correct graph.