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Trigonometry, 2ADV T1 2007 HSC 4c

 
An advertising logo is formed from two circles, which intersect as shown in the diagram.

The circles intersect at and and have centres at and .

The radius of the circle centred at is 1 metre and the radius of the circle centred at is metres. The length of is 2 metres.

  1. Use Pythagoras’ theorem to show that  .  (1 mark)

  2. Find    and  .  (2 marks)

  3. Find the area of the quadrilateral  .  (1 mark)

  4. Find the area of the major sector  .  (1 mark)

  5. Find the total area of the logo (the sum of all the shaded areas).  (2 marks)

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  3. ²
  4. ²
  5. ²
Show Worked Solution

i.

 
 
 

 

 

ii. 

 

iii. 

²

 

iv. 

 

 

²

 

v. 

 

²

 

²

Trigonometry, 2ADV T1 2012 HSC 13a

The diagram shows a triangle  . The line    meets the  and  axes at the points  and  respectively. The point  has coordinates  . 
 

2012 13a
 

  1. Calculate the distance  .   (2 marks)

  2. It is known that    and  (Do NOT prove this)  

     

    Calculate the size of  to the nearest degree.    (2 marks)

  3. The point lies on    such that    is perpendicular to  . 

     

    Find the coordinates of .    (3 marks)

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Show Worked Solution

i.   

 


  

 
 
 

 

ii.   

   
 
 
 
 
 

 

iii. 

½

 

½

MARKER’S COMMENT: Many students could not find the correct equation on because they took its gradient to be the reciprocal of and not the negative reciprocal. 
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