Add Maths Trigo R-Formula Help.

• Nathpoop

  1 Dec 09, 23:04

    

  Qn1: The diagram shows a trapezium PQRS. The point T lies on the side QR such that PT = 15cm, ST = 8cm, anglePTS = 90deg and angleTPQ = θ.

  (a) Show that QR = 15sinθ + 8cosθ and express it in the form Rsin(θ + a)

  Part (a) completed got the ans, ans: QR = 17sin(θ + 28.0725) and shown.

  (b) Find the value of θ for which QR has a maximum length.

  

   Qn2: The above diagram shows the side view of a bus stop shelter BCD such that BC = 4m, CD = 1m, angleBCD = 90deg and angleCBA = θ. AB is a concrete pavement under a shelter such that DA is perpendicular to AB

  (i) Show that AB = 4cosθ + sinθ

  (ii) Express AB in the form Rcos(θ - a), where R is +ve and a is an acute angle.

  Sorry for asking the qns, cause i'm new to this topic and not familar with this type of the qns, thanks in advance. Need help for both qns. (:

• Forbiddensinner

  2 Dec 09, 00:36

  Originally posted by Nathpoop:

    

  Qn1: The diagram shows a trapezium PQRS. The point T lies on the side QR such that PT = 15cm, ST = 8cm, anglePTS = 90deg and angleTPQ = θ.

  (a) Show that QR = 15sinθ + 8cosθ and express it in the form Rsin(θ + a)

  Part (a) completed got the ans, ans: QR = 17sin(θ + 28.0725) and shown.

  (b) Find the value of θ for which QR has a maximum length.

  

   Qn2: The above diagram shows the side view of a bus stop shelter BCD such that BC = 4m, CD = 1m, angleBCD = 90deg and angleCBA = θ. AB is a concrete pavement under a shelter such that DA is perpendicular to AB

  (i) Show that AB = 4cosθ + sinθ

  (ii) Express AB in the form Rcos(θ - a), where R is +ve and a is an acute angle.

  Sorry for asking the qns, cause i'm new to this topic and not familar with this type of the qns, thanks in advance. Need help for both qns. (:

  Hints:

  1(b)

  Maximum length = When sin (θ + 28.0725) is 1.

  sin (θ + 28.0725) = sin (θ + 28.0725 - 2pi) = sin (θ + 28.0725 - 4pi)... so on and so for.

   

  2(i)

  Draw a perpendicular line from C to AB.Let the intersection point be X. 

  Note that angle XCD = θ, and AX is of the same length as another "non-existant line".

   

  2(ii)

  This shouldn't be a problem once you solve part (i).

• SBS n SMRT

  2 Dec 09, 13:12

  R formulae is one of my favourite topics in AM

  Tips of proving

  • Using basic trigo properties
  • Cosine or sine rule
  • (Seldom) Draw a line here and there

  better to show full workings

• SBS n SMRT

  2 Dec 09, 13:33

  full working is the expansion of the R(cos x + sin x) formulae, plus the comparison of coefficients of cos x sin x etc, plus the R^2 = e.g. 169 and tan x = , blah blah