Sum and Difference Identities Worksheet

Sum and Difference Identities Worksheet
  • Page 1
 1.  
Find the value of cos 8° cos 4° + sin 8° sin 4°.
a.
0.9781
b.
0.9975
c.
1


Solution:

cos 8° cos 4° + sin 8° sin 4°

= cos (8° - 4°)
[Use cos A cos B + sin A sin B = cos (A - B).]

= cos 4° = 0.9975


Correct answer : (3)
 2.  
sin 33° = ?
a.
0.4675
b.
0.0769
c.
0.5444


Solution:

sin 33° = sin (5° + 28°)

= sin 5° cos 28° + cos 5° sin 28°
[Use sin (A + B) = sin A cos B + cos A sin B.]

= (0.0871)(0.8829) + (0.9961)(0.4694) = 0.5444


Correct answer : (4)
 3.  
cos 16° = ?
a.
0.9610
b.
0.9372
c.
0.0238


Solution:

cos 16° = cos (4° - 20°)

= cos 4° cos 20° + sin 4° sin 20°
[Use cos (A - B) = cos A cos B + sin A sin B.]

= (0.9975)(0.9396) + (0.0697)(0.3420) = 0.9610


Correct answer : (1)
 4.  
cos 28° = ?
a.
0.0283
b.
0.8829
c.
0.9112


Solution:

cos 28° = cos (4° + 24°)

= cos 4° cos 24° - sin 4° sin 24°
[Use cos (A + B) = cos A cos B - sin A sin B.]

= (0.9975)(0.9135) - (0.0697)(0.4067) = 0.8829


Correct answer : (3)
 5.  
tan (12 ) = ?
a.
3 - 2
b.
- 2 - 3
c.
2 + 3
d.
2 - 3


Solution:

tan (12 ) = tan (π4 + π6 )

= tanπ4 + tanπ61 - tanπ4tanπ6
[Use tan (A + B) = tan A + tan B1 - tan A tan B.]

= 1+331-33 = 3+33-3

= 3+33-3 · 3+33+3

= 9 + 63 + 39 - 3

= 12 + 636

= 2 + 3


Correct answer : (3)
 6.  
Find sin 9A cos 6A + cos 9A sin 6A .
a.
sin 3A
b.
cos 15A
c.
sin 15A
d.
cos 3A


Solution:

sin 9A cos 6A + cos 9A sin 6A

= sin (9A + 6A)
[Use sin A cos B + cos A sin B = sin (A + B).]

= sin 15A


Correct answer : (3)
 7.  
sin (5π + 6θ) = _________
a.
- cos 6θ
b.
sin 6θ
c.
cos 6θ
d.
- sin 6θ


Solution:

sin (5π + 6θ) = sin 5π cos 6θ + cos 5π sin 6θ
[Use sin (A + B) = sin A cos B + cos A sin B.]

= (0)cos 6θ + (- 1)sin 6θ

= - sin 6θ


Correct answer : (4)
 8.  
Find sin 70°30′ cos 10°30′ - cos 70°30′sin 10°30′.
a.
12
b.
sin 81°
c.
32
d.
cos 81°


Solution:

sin 70°30′ cos 10°30′ - cos 70°30′sin 10°30′

= sin (70°30′ - 10°30′)
[Use sin A cos B - cos A sin B = sin (A - B).]

= sin 60° = 32


Correct answer : (3)
 9.  
Evaluate: cos 5° cos 4° - sin 5° sin 4°
a.
1
b.
-1
c.
0.9876


Solution:

cos 5° cos 4° - sin 5° sin 4°
[Use cos A cos B - sin A sin B = cos (A + B).]

= cos (5° + 4°)

= cos 9° = 0.9876
[Check using calculator.]


Correct answer : (3)
 10.  
Find the value of sin 13° cos 9° + cos 13° sin 9°.
a.
0.0697
b.
0.3746
c.
1


Solution:

sin 13° cos 9° + cos 13° sin 9°
[Use sin A cos B + cos A sin B = sin (A + B).]

= sin (13° + 9°)

= sin 22° = 0.3746
[Check using calculator.]


Correct answer : (2)

*AP and SAT are registered trademarks of the College Board.