Wynberg girls high-louise keegan-maths-grade11-trigonometry revision

Mathematics Revision Gr 11 Trigonometry

Trigonometric Ratios y- axis x- axis P ( x : y ) A r

CAST Diagram A LL C OS S IN T AN

Example 1 x Work out sinA, cosA and tanA A (-4; 3) y

Example 2 ,[object Object],[object Object],[object Object]

Example 3 ,[object Object],[object Object],[object Object],[object Object],[object Object]

Steps to help you ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Special Angles ,[object Object],[object Object],[object Object],[object Object]

0 º, 90º, 180º, 270º, 360º

30º, 45º, 60º ,[object Object],[object Object]

Trig ratios (Using Triangles) A Hypotenuse Adjacent Opposite

Special Angles: Quick Test ,[object Object]

Reduction Formulae 1: ,[object Object],sin(360 º + A) = sinA cos(360 º + A) = cosA tan(360 º + A) = tanA

Reduction Formulae 2: ,[object Object],Ө

Reduction Formulae 3: ,[object Object],[object Object]

Reduction Formulae 3: ,[object Object],Ө (x,y) sin and cos are co-functions

Reduction Formulae Summary: Sin All (180 º - Ө ) Ө ( Ө ± 360 º) (90 º + Ө ) (90 º - Ө ) Tan Cos (180 º + Ө ) (360 º - Ө ) - Ө

Trig Identities: ,[object Object],[object Object],[object Object],[object Object],y x r

Identities examples: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Calculator Work: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Calculator Work: Equations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Using your calculator to find the reference angle:

Equations ,[object Object],[object Object],[object Object]

General vs. Specific Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Equations examples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Find the general solutions for the following equations:

More complex equations eg.s: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

sin, cos and area rules ,[object Object],[object Object],[object Object]

Example 1: (sin rule) ,[object Object],A C B 76 º b = 5,5 cm

Example 2: (cos rule) ,[object Object],D F E 9 cm 15 cm 8 cm

Example 3: cos rule ,[object Object],P R Q 120 º 5 cm 3 cm

Example 4: area rule ,[object Object],45 º 12 m 14 m

Extra examples: ,[object Object],[object Object]

Trig Functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Transformations on functions: Translation Enlargement Reflection +: Moves up -: Moves down +: Moves left -: Moves right Stretches y-values i.e. changes amplitude Stretches x-values i.e. changes period a<0 Reflects over x -axis

Wynberg girls high-louise keegan-maths-grade11-trigonometry revision

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