Trigo R-Formulae Qns.

• Nathpoop

  7 Dec 09, 02:54

  

  1. The diagram shows a right-angled triangle ABC in a semi-circle, centre O and radius 1cm. C is a point on the circumference such that angleCAB = xdeg. An equilateral triangle CND is drawn on the side BC. The area of the quadrilateral ABDC is S cm2.

  (a) Show that S = sin2x - ((Sqrt3)/2)cos2x + ((Sqrt3)/2).

  (b) Express sin2x - ((Sqrt3)/2)cos2x in the form Rsin(2x-a), where R>0 and a is acute.

  Thanks for helping.

  Rgds,

  Nathpoop.

   

• Forbiddensinner

  7 Dec 09, 06:00

  Originally posted by Nathpoop:

  

  1. The diagram shows a right-angled triangle ABC in a semi-circle, centre O and radius 1cm. C is a point on the circumference such that angleCAB = xdeg. An equilateral triangle CND is drawn on the side BC. The area of the quadrilateral ABDC is S cm2.

  (a) Show that S = sin2x - ((Sqrt3)/2)cos2x + ((Sqrt3)/2).

  (b) Express sin2x - ((Sqrt3)/2)cos2x in the form Rsin(2x-a), where R>0 and a is acute.

  Thanks for helping.

  Rgds,

  Nathpoop.

   

  (a)

  S = Area of ABC + Area of BCD

  Area of ABC = 1/2 X AC X BC

  Hints: sin ( 90 - x ) = cos x   and   sin2x = 2sinxcosx

  Area of BCD = 1/2 X BC X BD X sin 60

  Hints: a(sin x)^2 = a[1 - (cos x)^2] = -a(cos x)^2 + a

   

  (b)

  You don't seem to have any problem here from your previous questions. If the 2x is bothering you, just treat it as y, and sub 2x back in when you have simplify the entire thing.

   

  Edit: The equilateral triangle is simply CBD btw.