CHAPTER 10. TRIGONOMETRY 10.3
(a) Find AOCˆ in terms of θ.
(b) Find an expression for:
i. cosθ
ii. sinθ
iii. sin 2θ
(c) Using the above, show that sin 2θ =
2 sinθ cosθ.
(d) Now do the same for cos 2θ and tanθ.
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- DC is a diameter of circle O with radius r. CA = r, AB = DE and DOEˆ = θ.
Show that cosθ =^14.
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- The figure below shows a cyclic quadrilateralwithBCCD=ADAB.
(a) Show that the area of the cyclic quadrilateralis DC .DA. sinDˆ.
(b) Find expressions for cosDˆ and cosBˆ in terms of the quadrilateral sides.
(c) Show that 2 CA^2 = CD^2 +DA^2 +AB^2 +BC^2.
(d) Suppose that BC = 10, CD = 15, AD = 4 and AB = 6. Find CA^2.
(e) Find the angleDˆ using your expression for cosDˆ. Hence find the area of ABCD.
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