Understanding Engineering Mathematics

(やまだぃちぅ) #1

  • the sine and cosine rules and solution of triangles

  • graphs of the trig functions

  • inverse trig functions

  • the Pythagorean identities such as


cos^2 θ+sin^2 θ= 1


  • compound angle formulae such as


sin(A+B)=sinAcosB+sinBcosA

and their consequences such as the double angle formulae


  • solution of simple trig equations

  • Theacosθ+bsinθform


Motivation
You may need the material of this chapter for:


  • solution of triangles in statics, surveying, etc.

  • describing, analysing and combining oscillations and waves (➤Chapter 17)

  • evaluating trig and other integrals (➤Chapter 9)

  • describing angular motion

  • describing alternating current circuits


6.1 Review

6.1.1 Radian measure and the circle ➤173 194➤➤


A.Express as radians (i) 90° (ii)− 30 ° (iii) 45° (iv) 270° (v) 60°.


B. Express the following radian measures in degrees


(i)

5 π
6

(ii)

3 π
2

(iii) −

7 π
4

(iv) 4π (v) −

2 π
3

C.An arc of a circle of radius 2 subtends an angle of 30°at the centre. Find


(i) the length of the arc
(ii) the area of the sector enclosed by the arc and the bounding radii.

6.1.2 Definition of the trig ratios ➤174 194➤➤


Write down theexactvalues of the following (i.e. in surd form)


(i) cos 0 (ii) cos 2π (iii) sin 90°
(iv) sin

π
4

(v) cos

π
2

(vi) sin 45°

(vii) tan 90° (viii) sin 0 (ix) sin 60°
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