IB+Higher+Level+-+Circular+functions+and+Trigonometry

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The syllabus has remained largely the same here, some features such as applications of trigonometry have been more explicitly stated in the content, so the following is a slight amalgam of the two syllabi. Any significant differences are highlighted in bold.

3.1

The circle; radian measure of angles; length of an arc; area of a sector

3.2

Definition of //cos 0 // and //sin//// 0 // in terms of the unit circle.

Definition of //tan//// 0 // as //sin//// 0 /////cos//// 0 //


 * Exact values of trigonometric rations of 0,pi/6, pi/4, pi/3, pi/2 and their multiples**

Definition of //sec//// 0 //, //csc//// 0 //, and //cot//// 0 ////.//

Pythagorean identities: cos 2 // 0 // + sin 2 // 0 // = 1; 1 + tan 2 // 0 // = sec 2 // 0 //; 1 + cot 2 // 0 // = csc 2 // 0 //

3.3

Compound angle identities.

Double angle identities

3.4

The circular function //sinx, cosx// and //tanx// : their domain and ranges; their periodic nature and their graphs.

Composite functions of the form

//f(x) = asin(b(x+c) + d//

Applications

The inverse functions x |-> arcsinx, x |-> arccosx, x |-> arctanx; their domains and ranges; their graphs //**(chapter 3.5 in new syllabus)**//

3.5 //**(chapter 3.6 in new syllabus)**//

Solution of trigonometric equations in a finite interval.

Use of trigonometric identities and factorization to transform equations.

3.6 //**(chapter 3.7 in new syllabus)**//

Solution of triangles

The cosine rule: //c// 2 //= a// 2 //+ b// 2 //- 2abcosC//

The sine rule: //a/sin A = b/SinB = c/SinC// (including the ambiguous case)

Area of a triangle as 1/2absinC

Applications

Pages relating to Circular functions and trigonometry
and similar with cosine and tangent functions || 3.4 || J. Gregg ||
 * **Page Name** || **Description** || **Chapter ref.** || **Added by** ||
 * Transforming Trig Functions || Use GeoGebra to investigate functions of the form y = asin(bx + c) + d,