Download Practice 9-4

Trig Identities Sum and Difference
Page 1 of 4
Teacher: Mrs. Russolello
Name: ____________________________________
Sum and Differences Identities
Practice 9-4
1.
5.
Express sin 75° cos 15° cos 75° sin 15° as a single The expression tan (180° + x) is equivalent to
trigonometric function of a positive acute angle.
1. cot x 3. -cot x
1. cos 60°
2. tan x 4. -tan x
2. cos 85°
-------------3. sin 60°
4. sin 85°
6.
--------------
If tan A = 8 and tan B =
2.
The expression cos 80° cos 20°
equivalent to
1.
2.
3.
4.
sin 80° sin 20° is
cos 60°
cos 100°
sin 100°
sin 60°
(A + B)?
1. 4/3
2. 17/10
3. -15/6
4. -17/6
--------------
7.
--------------
3.
The expression sin 50° cos 40° + cos 50° sin 40° is
equivalent to
1.
2.
3.
4.
, what is the value of tan
The value of cos 75° cos 15°
sin 75° sin 15° is
1. 1
2.
3.
sin 10°
cos 10°
sin 90°
cos 90°
4. 0
---------------------------
4.
The expression sin (180°
1. sin x
2. cos x
x) is equivalent to
3. -sin x
4. -cos x
--------------
http://castlelearning.com/review/teacher/AssignmentPrinting.aspx
3/15/2012
Trig Identities Sum and Difference
Page 2 of 4
8.
11.
Since sin 75° = sin (30° + 45°), then sin 75° equals
Find m
in the interval 180°
270° that
satisfies the equation 2cos + 1 = 0.
1. 210°
2. 235°
3. 240°
4. 260°
--------------
12.
180°, find the value of
In the interval 90°
satisfies the equation 2 sin
1 = 0.
--------------
1. 30°
2. 120°
9.
that
3. 150°
4. 175°
--------------
If A and B are positive acute angles, sin A =
cos B =
, and 13.
, what is the value of sin (A + B)?
If f (x) = sin2 x + cos2 x, find f ( ).
1.
1. 1
2. 2
2.
3.
3.
4. 0
--------------
4.
14.
--------------
10.
The expression cos 40° cos 10° + sin 40° sin 10° is
equivalent to
1. cos 30°
2. cos 50°
3. sin 30°
4. sin 50°
Which expression is equivalent to sin 22° cos 18° +
cos 22° sin 18°?
1.
2.
3.
4.
sin 4°
cos 4°
sin 40°
cos 40°
--------------
--------------
http://castlelearning.com/review/teacher/AssignmentPrinting.aspx
3/15/2012
Trig Identities Sum and Difference
15.
The expression cos
1.
2.
3.
4.
(sec
1
sin
sin2
-cos2
Page 3 of 4
19.
An architect is using a computer program to design
cos ) is equivalent to the entrance of a railroad tunnel. The outline of the
opening is modeled by the function f(x) = 8 sin x + 2,
in the interval 0 x
, where x is expressed in
radians.
(a) Solve algebraically for all values of x in the
interval 0 x
, where the height of the opening, f
(x), is 6. Express your answers in terms of and in
increasing order
--------------
16.
Express sin 150° as a function of a positive acute
angle.
1.
2.
3.
4.
sin 30°
cos 30°
sin 60°
-cos 60°
Answer:
and
(b) If the x-axis represents the base of the tunnel,
what is the maximum height of the entrance of the
tunnel?
Answer:
units
--------------
--------------
17.
If cos x = 12/13 and sin y = 4/5, then sin (x
equals
1. 72/65
2. 56/65
y)
3. -16/65
4. -33/65
--------------
18.
What is the total number of solutions for the equation
3 tan2 A + tan A 2 = 0 in the interval 0 A
?
1.
2.
3.
4.
5.
1
2
3
4
0
--------------
http://castlelearning.com/review/teacher/AssignmentPrinting.aspx
3/15/2012
Trig Identities Sum and Difference
Page 4 of 4
Answer Key for Trig Identities Sum and Difference
1. 3
2. 2
3. 3
4. 1
5. 2
6. 4
7. 4
8. 4
9. 1
10. 1
11. 3
12. 3
13. 1
14. 3
15. 3
16. 1
17. 4
18. 2
19. 1/6, 5/6, 10
http://castlelearning.com/review/teacher/AssignmentPrinting.aspx
3/15/2012