Friday, 15 June 2012

TRIGONOMETRY {Trig Identities}

TRIGONOMETRY  {Trig Identities}
The sine, cosine and area rules are introduced in grade 11, as well as problems in two dimensions.

The identities:                Remember
tan2θ = sin2 θ/cos2 θ        sin A = opp / hyp   = a / c
sin2θ+cos2θ = 1              cos A = adj / hyp  = b / c
                                        sin2 A   +   cos 2 A
                                        =  (a/c) 2   +  ( b/c)2


1.   Simplify:

(a)       sin(1800 +A)
cos(1800 - A)

       (b)         cos (900 + A)               .
    tan(1800 – A).cos( 3600+A)


2.     Prove the following identities:

      (a)         8              4         =       4       
Sin2A    1+cos A        1-cos A
                   
      (b)         cos²A           1       +     1            =    – 2 sin A             
                                          sinA -1)     sinA +1)
   
3.      Given that cos 58°= k, find the following in terms of k, without
         using a calculator:

(a)     sin 212°
(b)tan(-58°)

(c)      sin 148°


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1 comment:

  1. manoj singh15 June 2012 at 23:14

    Thanks for such a great information.Scientific fields that make use of trigonometry include:
    acoustics, architecture, astronomy , cartography, civil engineering, geophysics, crystallography, electrical engineering, electronics, land surveying and geodesy, many physical sciences, mechanical engineering, machining, medical imaging , number theory, oceanography, optics, pharmacology, probability theory, seismology, statistics, and visual perception
    That these fields involve trigonometry does not mean knowledge of trigonometry is needed in order to learn anything about them. It does mean that some things in these fields cannot be understood without trigonometry. For example, a professor of music may perhaps know nothing of mathematics, but would probably know that Pythagoras was the earliest known contributor to the mathematical theory of music.Exponential Distribution

    ReplyDelete

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