Download PreCalculus Semester 2 Review

PreCalculus
Semester 2 Review
Use a separate sheet of paper to do your work.
1. a) Convert to degrees:
7
12
b) Convert to radians: 27°
4.1
2. A man that is 6 feet tall casts a shadow 10 feet long. Find the angle of elevation of the sun
4.3
3. Use trigonometric identities to simplify the expression:
4.3/5.1
a) 1  cos  1  cos  
c)
b) cot 2 x sin 2 x
sin 2 
cos 2 


d) sec 2 x  1 cot 2 x
3
4. Given sin   and tan  0 , find cot 
5
4.4
5. Graph each equation.
4.5
1 
(a) y  cos x 
2 
(b) y  sin4 x   1
(c) y  cos 2 x  4
(d) y  3 sin
6. Evaluate:
 3

a) arcsin 

2


x
4
4.7
 2

b) arccos 

2


c) arctan 1

 2 
7. Evaluate: sin arccos   
 3 

8. Simplify: a) sec x 
sin 2 x
cos x
9. Simplify: sin x  cot x cos x
4.7
b)
1
1
sin 2 x
5.1
5.1
10. Evaluate:
a) sin
5.4
11
11 3 
, Use the fact that


12
12
4 6
b) cos 105, Use the fact that 105  60  45


11. Simplify: cos   
2

5.4
12. Find all the solutions in the interval 0,2  : 2 sin x  2  0
5.3
13. Find all the solutions in the interval 0,2  : cot x cos 2 x  2 cot x
5.3
14. Find all the solutions in the interval 0,2  : sin 2 x  cos x  0
5.3/5.5
15. Find all the solutions in the interval 0,2  : tan 2 x  3  0
5.3
16. Find the area of the triangle.
6.2
6
8
12
17. Find the value of x.
6.1
10
12
46º
x
18. a = 10, b = 4.5, C = 105°
Find side c.
6.2
19. B = 150°, a = 10, c = 20 Find angle A.
6.2
20. B = 110°, a = 125, b = 100 Find side c.
6.1
21. Find the value of x for the following 45° - 45° - 90° triangles.
x
6 2
x
10
3
3
x
x
22. Find the value of x for the following 30° - 60° - 90° triangles.
x
10 3
4 3
x
x
x
8
14
23. Find the vertex, focus, and directrix of the parabola: x 2  6 x  4 y  5  0
9.1 – 9.3 ↓
24. Find the standard equation of the parabola with its vertex at (2, 1) and its focus at (2, 4).
25. Find the center of the ellipse: 9 x 2  5 y 2  36 x  30 y  36  0
26. a) Find an equation of an ellipse with foci (0, 1) and (4, 1) and major axis of length 6.
b) Find an equation of an ellipse with foci (-1, 1) and (-1, 9) and major axis of length 10.
27. Graph:
28. Graph:
x  32
25

y2
1
49
 y  12  x  42
4
25
1
29. Find the center and foci of the hyperbola: x 2  9 y 2  10 x  18 y  7  0
30. Identify the graph of each conic: 2 x 2  2 y 2  12 x  4 y  9  0
x 2  6x  2 y  9  0
3x 2  6 x  3 y 2  12 y  8  0
4 x 2  y 2  16 x  15  0