• Home
  • Textbooks
  • Engineering Mathematics Through Applications
  • Trigonometry and Waveforms

Engineering Mathematics Through Applications

Kuldeep Singh

Chapter 4

Trigonometry and Waveforms - all with Video Answers

Educators

Section 1

Trigonometric functions

01:27

Problem 1

Evaluate the following to 2 d.p.: $\sin \left(35^{\circ}\right), \cos \left(47^{\circ}\right)$ and $\tan \left(21^{\circ}\right)$

Steven Clarke
Steven Clarke
Numerade Educator
01:17

Problem 2

By using Table 1, find the exact values of the following:
i $\cos \left(45^{\circ}\right) \sin \left(45^{\circ}\right)$
ii $\tan \left(60^{\circ}\right)+\tan \left(30^{\circ}\right)$
iii $\sin \left(60^{\circ}\right)+\tan \left(60^{\circ}\right)$
iv $\frac{\sin \left(45^{\circ}\right)}{\tan \left(45^{\circ}\right) \cos \left(45^{\circ}\right)}$
v $\cos \left(45^{\circ}\right)+\sin \left(60^{\circ}\right)$
vi $\sin \left(60^{\circ}\right) \cos \left(30^{\circ}\right)+\cos \left(60^{\circ}\right) \sin \left(30^{\circ}\right)$

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
01:41

Problem 3

Figure 13 shows a symmetrical roof truss, with rise $r=4 \mathrm{~m}$ and rafter AC inclined at $25^{\circ}$.
Evaluate the length of the rafter AC and span $\mathrm{AB}$.

Jonathon Brumley
Jonathon Brumley
Numerade Educator
01:58

Problem 4

By using $\sin (\theta)=\frac{o p p}{h y p}$ and $\cos (\theta)=\frac{a d j}{h y p}$ show that $\tan (\theta)=\frac{\sin (\theta)}{\cos (\theta)}$.

Urvashi Arora
Urvashi Arora
Numerade Educator
01:42

Problem 5

Figure 14 shows a garage roof with $r=3 \mathrm{~m}$ and $s=6 \mathrm{~m}$. Find the size of the angle $\theta$.

Dwijendra Rao
Dwijendra Rao
Numerade Educator
02:16

Problem 6

Figure 15 shows a symmetrical part of a bridge lattice. Determine the length $h$, given that $\mathrm{AD}=5 \mathrm{~m}$, angle $\mathrm{DAB}=55^{\circ}$ and $X$ is the midpoint of $\mathrm{ABCD}$.

Jay Patel
Jay Patel
Numerade Educator
02:54

Problem 7

Figure 16 shows a cross-section of a rain gutter with $\mathrm{PQ}=\mathrm{QR}=\mathrm{RS}=180 \mathrm{~mm}$ and angle $\theta=60^{\circ}$. Find the area of the cross-section PQRS.

William Semus
William Semus
Numerade Educator
00:08

Problem 8

Determine the value of $x$ in each of the following cases:

Amy Jiang
Amy Jiang
Numerade Educator
02:04

Problem 9

Without using a calculator, find the five other trigonometric ratios [including $\sec (\theta), \operatorname{cosec}(\theta)$ and $\cot (\theta)]$ given:
i $\sin (\theta)=\frac{1}{\sqrt{3}} \quad$ ii $\cos (\theta)=\frac{2}{3}$
iii $\tan (\theta)=\frac{3}{4}$

Julie Silva
Julie Silva
Numerade Educator
02:40

Problem 10

Evaluate the following to 3 d.p.:
$$
\sec \left(36.4^{\circ}\right), \cot \left(29.17^{\circ}\right)
$$
and $\operatorname{cosec}\left(44.44^{\circ}\right)$

Mohamed Mohamed
Mohamed Mohamed
Numerade Educator
00:30

Problem 11

By using any mathematical software plot the following graphs between $0^{\circ}$ and $360^{\circ}$.
a $y=\operatorname{cosec}(\theta)$
b $y=\sec (\theta)$
c $y=\cot (\theta)$

Linh Vu
Linh Vu
Numerade Educator