UPREP Trig Math Workbook Grade 11

Telechargé par Lerato Lerato
TRIGONOMETRY
here
Tara Conradie
Grade 11
23 July 2022
TRIGONOMETRY
NB - make sure your calculator is on ‘DEG
1. DEFINITIONS, IDENTITIES & RULES:
1.1 Definitions:
For any size :
 


 





1.2 Identities:
  
cos
sin cos  
1.3  Rule:
1) Determine the quadrant
2) Use CAST diagram to determine the sign
3) Keep the same ratio (sin, cos or tan), but
possibly change the sign.
e.g.  
because  is in the 3rd
quadrant, where sine is negative
1.4  Rule:
   
    









2. SPECIAL ANGLES:
2.1 Special triangles:
Know the 45/30/60 ratios without a
calculator.
Use calculator for 0/90/180/270/360


  



 
 
2.2 Combined with and rules:
ALWAYS first reduce to an acute angle.
e.g.  




3. USING SKETCHES:
3.1 If    , use a sketch (and not a
calculator) to find  if
   
Must be quadrant 3 where cos is negative.
Use Pythagoras to calculate .
Watch out for the sign.
3.2 If 
, write sin in terms
of .
Draw a right-angled triangle and fill in
and on the opposite and adjacent
sides.
Use Pythagoras to calculate the 3rd side.
sin2


4. TRIG EQUATIONS:
4.1
Equations must be manipulated to give:
Watch out for   the number   for
sin / cos
First find the help-angle:
Then use CAST-diagram to determine
quadrants where positive or negative.
sin / cos /  a number
SHIFT-button (don’t push minus)
4.2
General solution:
Interval given:
sin / cos :   
tan :   
Find all angles in interval by substituting
   etc

Y
X
  , therefore   

4.3
  
  
Divide by  to get 
Use the  rule to change sin ↔ cos
4.4 Factorising:
eg.   
eg. sin2 cos  
eg. sin  cos2  
eg.  cos  
Common factor
Difference of squares
Trinomial
Grouping
Sum & Difference of cubes
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UPREP Trig Math Workbook Grade 11

Telechargé par Lerato Lerato
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