PreCalculus
1.
Extra Practice for Test 4.5, 4.7, 4.8
Find the exact value of the expression
sec arctan
2016
3
4
(draw a triangle)
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2.
Write an algebraic expression that is equivalent to
sin arctan
x
8 .
(draw a triangle)
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3. From a point 40 feet in front of a church, the angles of elevation to the base of the steeple
and the top of the steeple are 30 and 47 10', respectively. Find the height of the steeple.
Round your answer to the nearest hundredth.
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4.
The displacement from equilibrium of an oscillating weight suspended by a spring is given by
the following function,
y t
2e t cos 9t
where y is the displacement (in centimeters) and t
is the time (in seconds). What is the initial displacement
nearest hundredth.
t
0 ?
Round your answer to the
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5.
Find a and d for the function f ( x)
a sin x d such that f ( x) matches the graph below.
PreCalculus
Extra Practice for Test 4.5, 4.7, 4.8
6. The diagram shows a pyramid VABCD which has a square base of length 10 cm and edges of
length 13 cm. M is the midpoint of the side BC.
(a)
Calculate the length of VM.
(b)
Calculate the vertical height of the pyramid
(c)
Calculate the angle between a sloping face of the pyramid and its base.
2016
True or False
7. ___________
The sine curve has an intercept at (π,0).
8. ___________
The graph of y = 3sinx + 2 is shifted up two units.
9. ___________
The cosine curve has a maximum at (π, 1)
10. ___________
The graph y = 4cos(2x + 4) + 3 has a phase shift of 2 to the right.
11. ___________
The phase shift stretches the graph horizontally.
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12. Write the sine function for the curve that has an amplitude of 5, a period of 4 , a phase shift of
2
to the right and a vertical shift of 6 units down.
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Given y
3cos(2 x
2
).
13. What is the amplitude?
14. the period?
15. the phase shift?
16. Sketch accurately, labeling EVERYTHING!
Also study the two worksheets Graphs of Sine and Cosine, homework and classwork problems.