Write down the exact value of cos .
Write down the exact value of cos .
Use your calculator to find the exact value of cos .
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Write down the exact value of cos .
Write down the exact value of cos .
Use your calculator to find the exact value of cos .
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Express sin in terms of sin and sin .
Hence show that
sinÂ
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Starting with the identity
      sinsin cos sin cosÂ
And using the substitution , show that sin sin cos .
Hence show the exact value of sin .
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Use an appropriate identity to find sin in terms of sines and cosines of and .
Hence show that sin cos sin sin cos .
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Solve the following equations in the given intervals.
sinÂ
cosÂ
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Show that
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Show that
           Â
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Show that ,    where  and are constants with  and .
Write down the maximum value of .
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Sketch the graph of  for .
Label the points at which the graph intersects the coordinate axes.
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Use the difference of two squares to show that
              Â
Hence solve the equation
           Â
for .
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Prove by a counter-example that sinsin sin  is not true in general.
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Express tan in terms of tan and tan
Hence show that tan.
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Starting with the identity
          coscos cos sin sinÂ
and using the substitution , show that cos cos2 sin2Â
Hence, or otherwise, show that cos sin2 .
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Using an appropriate trigonometric identity, show thatÂ
        Â
where  and  are constants.
Hence show that .
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Use appropriate double angle formulae to solve the following equations in the given intervals.
cos2Â sin2Â Â Â Â
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Show that
           Â
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Show that , where and are constants.
Hence solve the equation cos sin for .
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Using the identities
            sin sin cos sin cos  and
           cos sin2Â
show that sin sin sin3Â
Hence, or otherwise, solve the equation
            sin sin3Â
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Show that can be written in the form where and .
Sketch the graph of sin cos for .
Label any points where the graph intercepts the coordinate axes.
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Show that cosec cosec sec .
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If , then
      sinsinsinsin sin sin sinÂ
By using a suitable counter-example with , prove that sinsin sin is not true in general.
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Express cos in terms of cosines and sines of 315° and 30°.
Hence show that cos.
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Show that
      sin sin cosÂ
(You may use the identity sin sin cos cos sin .)
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Show that cos sin   can be written in the form  cos, where  and  are constants with    and    .
Give  in the form  where  is an integer, and give  correct to three significant figures.
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Solve the equation
         sin sin       Â
Solve the equation
         cos sin2      Â
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Show that
           Â
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Show that can be written as  , where  to three significant figures.
Hence solve the equation
         sin cos
giving your answers correct to 3 significant figures.
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By letting , use the identity for to derive an expression for in terms of tan .
Hence, or otherwise, solve the equation
        Â
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Sketch the graph of  for .
Be sure to label any points where the graph intercepts the coordinate axes, and state the coordinates of any maximum and minimum points.
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Show that
      cot tan sec2Â
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Prove that  is not true in general.
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Use the identities and  to show that
     Â
Hence show that .
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Show that
        Â
State clearly any trigonometric identities you use to show this result.
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Given that , where  and  are positive constants, is to be written in the form ,  find expressions for:
in terms of andÂ
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Solve the equation
        Â
Solve the equation
         tan tanÂ
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Show that
         tan tan secÂ
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Show that can be written in the form where   , and radians correct to three significant figures.
Use your result from part (a), and the properties of the sine and cosine functions, to solve the equation
           Â
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Use an identity for cos to derive an identity for cos , in terms of cos .
Hence, or otherwise, solve the equation
        Â
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The diagram below shows two right-angled triangles.
Angles  and  have been labelled.
Given that  , find the exact values of sin ,cos and tan .
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Explain briefly why is not a solution to the equation .
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