Math 5 Trigonometry  Final Exam  Fall ’06       Name_________________________

Show your work for credit.  Write all responses on separate paper.

1.      A right triangle with legs 8 and 15 is inscribed in a circle centered at the origin, as shown in the diagram. a.       Find the area of the shaded region. b.      Find the coordinates of P. 2.      Find an equation for the line tangent to the circle  at (5, 12).

3.      Find an equation for the line perpendicular to the line segment from (0,8) to (10,0) and passing through its center.

4.      Given the plot of  shown below, sketch a graph for

a.        

b.     

5.      Sketch a graph for the function

6.      The point P is on the unit circle is in QII and has y = .  Find the x coordinate of P.

7.      Find the amplitude, period and phase shift of  and construct a large, careful graph showing these features.  Remember to scale and label axes.

8.      Consider  

a.       Find the domain of the function.

b.      Find the range of the function.

c.       Sketch a graph of the function showing one period.  Remember to scale and label axes.

9.      A potter’s wheel with radius 6 inches spins at  180 rpm.  Find the angular and linear speeds of a point on the rim of the wheel in feet per second.

10.  In the figure at right, find x and y correct to the nearest hundredth. 11.  From a point A on the ground, the angle of elevation to the top of a tree is 28.1°.  From a point B, 17 feet closer, the angle of elevation is measured to be 34.2°.  Find the height H of the tree.  See below:

 

12.  Write the conic in standard form and sketch a graph indicating key features:

a.        

b.