Garden Grove Unified School District
Precalculus Quarter 2 Benchmark Review 2009-10
Scientific Calculators are permitted
7. In ABC , write an equation equivalent to
sin 2   cos 2   1.
y
Garden Grove Unified School District
Precalculus Qtr 2 Benchmark Review 2009-10
Scientific calculators are permitted
. Trig 4.0


A
1. On what interval of 0  x  2 is y  sin x
decreasing?
c
2. Which of the following is the graph of

y  2sin( 2x   ) ? Justifyyour answer.
5
b

-5
C

a
x
B
5

8. Starting with the identity, sin 2   cos 2   1,
Maria is proving that 1 tan 2   sec 2  . What is
the first step in her proof?


3
3
   2 and cos  , what is the
2
5
value of tan  ?
9. If
3. Write an equation for the cosine function that
has two consecutive maximum points at (3,4)
and (11, 4). The minimum value of the function
is –2.
Trig 3.0
4. What is the measure of the phase shift in the
equation, y  2cos4(t  5) ?
2
3
 10. If 0    and tan    , what is
4
sin?
 Trig 10.0

 11. Using a sum or difference identity, write the
first step in finding the exact value of sin 15°.
Then find the exact value (leave in radical form).
5. Simplify: tan x(1 sin x)

6. What is the value of tan xsin x in terms of the
cos x?


Precalculus Q2 Benchmark Review 2009-10
3

when
    and
5
2
12
3
, then what is the
cos   
when    
13
2
value of sin(   ) ?
12. If sin  
2



Garden Grove Unified School District
Precalculus Quarter 2 Benchmark Review 2009-10
Scientific Calculators are permitted
  
13. What is the exact value of cos  ?
3 4 
20. In order to find the exact value of the
cos 15° using the half angle identity for cosine,
which of the following would be the correct first
step?
5
and 0    90 , what is the
13
 ?
value of the sin(   90)
14. If sin  
15. Which of the following would not be 2
 values that could be used to find the exact value

5
of cos  using the sum or difference identity? 
12

 
A) cos(  )
6 4
2 
C) cos(  )
3 4
 11.0
Trig
1  cos30
2
1  cos 30
C) 
2

Trig 9.0
A)

 
B) cos(  )
6 4
3 
D) cos(  )
4 3
1 cos30
2
1 cos 30
D) 
2
B)

 2 
21. What is the value of Sin 1  in radians?
 2 
22. What is the range of f (x)  Cos1 (x) ?

3
16.
when
 If the cos  
 270° ≤  ≤ 360°.
2


3
23. What is the value of tanArc sin ?

5 

What is the value of sin ?
2


24. What are all the values of x, in radians, if
1
sin x   ? 
2

17. If cos  p and 0    90, what is
?
sin 2
Trig 13.0

18. What is the value of

sin 2  cos2 


5 ?
when 0   
and sin  
2
13
10

19. Jerry needs to derive a formula for cos .
2

2
He starts with the identity cos2x  2cos x 1.
Which of the following could be his next step?

a) divide both sides of the equation
by 2


b) multiply both side of the equation by
2
c) replace x with

2
d) replace x with 2 


25. What is x in the triangle shown? Round to
the nearest tenth.
110°
15
x
26. What is the value of x in the triangle with
dimensions as shown? Round your answer to the
nearest tenth.
70°
x
65°
7

Precalculus Q2 Benchmark Review 2009-10
Garden Grove Unified School District
Precalculus Quarter 2 Benchmark Review 2009-10
Scientific Calculators are permitted
27. In the triangle shown, what is x?
100°
12
x
28. To the nearest minute, what is the
approximate size of the smallest angle of a
triangle whose sides are 4, 5, and 8?
y


5

Trig 14.0
-5
29. Kim made a triangular garden in her
backyard bordering along the fence. What is the
area, to the nearest 0.01 of a square foot of the
garden?
65°
15’
30. The area of the triangle shown is 60 sq. ft.
What is the approximate measure of x to the
nearest tenth of a foot?
42°
Trig 7.0
33. What is the tan if  is the acute angle
shown in the diagram?
16
13’
32. In triangle ABC, a = 5, b = 7, c = 10. What
is the area of triangle ABC to the nearest square
unit?
5
x

-5
34. The equation of a line is 3x  4 y  10 .
What is the approximate measure of the acute
angle formed where the line intersects the xaxis?

35. If a line crosses the y-axis at (0, -2) with an
acute angle of 27°, what is an approximate
equation of the line?
y
15’
27°
x
31. A parallelogram has the dimensions shown.
Find the area to the nearest square foot.
50 ft
55°
70 ft
Precalculus Q2 Benchmark Review 2009-10
x
Garden Grove Unified School District
Precalculus Quarter 2 Benchmark Review 2009-10
Scientific Calculators are permitted
36. Two sides of triangle CDE are 9 and 4, as
shown. Write an equation in standard form for
the line CD. Leave values as radicals.
y

C
9
E
D
4
37. What is the measure and the direction of the
phase shift in the equation y  5cos(2t  4) ?

Precalculus Q2 Benchmark Review 2009-10
x
Garden Grove Unified School District
Precalculus Quarter 2 Benchmark Review 2009-10
Scientific Calculators are permitted
Answer Key












 3 
1.  , 
2 2 
2. A


3. y  3cos (x  3)1
4

4. 5 units to the right
5. sin 2 x
1 cos 2 x
6.
cos x
7. a 2  b 2  c 2
8. divide all terms by cos2 
4
9. 
3
3

10.
5
11. sin15  sin( 45  30) 
23.


27. 47.6°
28. 24°09’
29. 88.37 sq ft
30. 12.0 ft
6 2
4
2 3
2
17. 2p 1 p2
264
169
20. A
21.

rads
4
22. 0  f (x)  


31. 2,867 sq ft
32. 16 sq units
33. 
Precalculus Q2 Benchmark Review 2009-10
4
5
34. 37°

16.
19. C

25. 20.7
26. 5.3
16
65
2 6
13.
4
12
14.
13
15. A

7
11
 2k and
 2k where k is an
6
6
integer
24.
12. 
18.
3
4
35. y = 2x –2
36.
65x  4y  4 65
37. 2 units to the right
