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# Cos 2 x d uniformly replace x by θ 2 in the identity

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(x) in the identity for cos(2x) and then solve for cos 2 (x) in terms of what remains. cos 2 (x) = (d) Uniformly replace x by θ /2 in the identity for cos 2 (x) that you obtained in part (c) above in order to obtain an identity for cos 2 ( θ /2). Clean up the algebra. cos 2 ( θ /2) = (e) Modify steps (c) and (d) appropriately to obtain a corresponding identity for sin 2 ( θ /2). Show your work neatly. sin

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Final Exam/MAC1114 Page 7 of 8 24. (10 pts.) To measure the height of the top of a distant object , a surveyor takes two sightings of the top of the object 5000 feet apart. The first sighting, which is nearest the object, results in an angle of elevation of 45°. The second sighting, which is most distant from the object, results in an angle of elevation of 30°. If the transit used to make the sightings is 5 feet tall, what is the height of the object. You may assume the object is on a level plane with the base of the transit. 25. (15 pts.) Sketch the given curve in polar coordinates. Do this as follows: (a) Carefully sketch the auxiliary curve, a rectangular graph on the coordinate system provided. (b) Then translate this graph to the polar one. Equation: r=1+2 sin( θ ) (a) r θ (b) y x
Final Exam/MAC1114 Page 8 of 8 26. (10 pts.) Very carefully sketch the graph of the equation ( x+1 ) 2 = -4(y - 2) below. y x 27. (5 pts.) Use the Law of Sines to solve the triangle with α = 115°, γ =3 ,a n dc=3 . Y o um a y assume that the standard
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cos 2 x d Uniformly replace x by θ 2 in the identity for...

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