Cambridge Additional Mathematics

8 Contents: A Radian measure B Arc length and sector area C The unit circle and the trigonometric ratios The unit circle and rad ...

202 The unit circle and radian measure (Chapter 8) Opening problem Consider an equilateral triangle with sides 2 cm long. Altitu ...

The unit circle and radian measure (Chapter 8) 203 Historical note There are several theories for why one complete turn was divi ...

204 The unit circle and radian measure (Chapter 8) Example 2 Self Tutor Convert 126 : 5 ±to radians. 126 : 5 ± = (126: 5 £ 180 ¼ ...

The unit circle and radian measure (Chapter 8) 205 The diagram alongside illustrates terms relating to the parts of a circle. An ...

206 The unit circle and radian measure (Chapter 8) Example 4 Self Tutor A sector has radius 12 cm and angle 3 radians. Find its: ...

The unit circle and radian measure (Chapter 8) 207 8 The cone is made from this sector: Find, correct to 3 significant figures: ...

a LESS SPACE GIVEN!!! LESS SPACE GIVEN!!! 208 The unit circle and radian measure (Chapter 8) Theunit circleis the circle with ce ...

The unit circle and radian measure (Chapter 8) 209 In general, for a point P anywhere on the unit circle: ² cosμis thex-coordina ...

210 The unit circle and radian measure (Chapter 8) Discovery 1 The trigonometric ratios In this Discovery we explore the signs o ...

The unit circle and radian measure (Chapter 8) 211 PERIODICITY OF TRIGONOMETRIC RATIOS Since there are 2 ¼radians in a full revo ...

212 The unit circle and radian measure (Chapter 8) 3aUse your calculator to evaluate: i p^12 ii p 3 2 b Copy and complete the fo ...

The unit circle and radian measure (Chapter 8) 213 b In which quadrants are the following true? i cosμis positive. ii cosμis neg ...

214 The unit circle and radian measure (Chapter 8) EXERCISE 8D.1 1 Find the possible values ofcosμfor: a sinμ=^12 b sinμ=¡^13 c ...

The unit circle and radian measure (Chapter 8) 215 5 Find exact values forsinxandcosxgiven that: a tanx=^23 and 0 <x<¼ 2 b ...

If or is negative, your calculator will give in the domain. sin tan 0 μμ μ -___wp<μ< PARAMETRIC PLOTTER The arrow shows th ...

1 1 45 ° ~`2 P,(a a) x y 1 1 45° 45° a a B 1 O x y (0 1), (1 0), (0 -1), (-1 0), r_p Ef_p Uf_p Tf_p &-[[, * &[[, * & ...

218 The unit circle and radian measure (Chapter 8) MULTIPLES OF¼ 6 OR 30 ± Since OA=OP, triangle OAP is isosceles. The remaining ...

The unit circle and radian measure (Chapter 8) 219 Example 12 Self Tutor Find the exact values of sin®, cos®, and tan® for: a ®= ...

220 The unit circle and radian measure (Chapter 8) 5 Without using a calculator, evaluate: a sin^260 ± b sin 30±cos 60± c 4 sin ...