- 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+sinBcosAand 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
3C.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) sinπ
4(v) cosπ
2(vi) sin 45°(vii) tan 90° (viii) sin 0 (ix) sin 60°