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MATH1720HomeworkChapter5Section5

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Use an identity to write the expression as a single trigonometric function or as a single number.
 2 cos2 22.5° - 1
a.
mc001-1.jpg
c.
mc001-3.jpg
b.
mc001-2.jpg
d.
mc001-4.jpg
 

 2. 
Use an identity to write the expression as a single trigonometric function or as a single number.
sin 22.5° cos 22.5°
a.
mc002-1.jpg
c.
mc002-3.jpg
b.
mc002-2.jpg
d.
mc002-4.jpg
 

 3. 
Use an identity to write the expression as a single trigonometric function or as a single number.
mc003-1.jpg
a.
mc003-2.jpg
c.
mc003-4.jpg
b.
mc003-3.jpg
d.
mc003-5.jpg
 

 4. 
Use an identity to write the expression as a single trigonometric function or as a single number.
 mc004-1.jpg
a.
mc004-2.jpg
c.
mc004-4.jpg
b.
mc004-3.jpg
d.
mc004-5.jpg
 

 5. 
Use an identity to write the expression as a single trigonometric function or as a single number.
2 cos2 75° - 1
a.
- mc005-1.jpg
c.
mc005-3.jpg
b.
mc005-2.jpg
d.
- mc005-4.jpg
 

 6. 
Use an identity to write the expression as a single trigonometric function or as a single number.
sin 8x cos 8x
a.
mc006-1.jpg sin 16x
c.
2 sin 4x
b.
cos 4x
d.
cos 8x
 

 7. 
Use an identity to write the expression as a single trigonometric function or as a single number.
 cos24x - sin24x
a.
2 sin 4x
c.
mc007-1.jpg sin 16x
b.
cos 4x
d.
cos 8x
 

 8. 
Use an identity to write the expression as a single trigonometric function or as a single number.
4 sin 2x cos 2x
a.
cos 8x
c.
2 sin 4x
b.
cos 4x
d.
mc008-1.jpg sin 16x
 

 9. 
Use an identity to write the expression as a single trigonometric function or as a single number.
 1 - 2 sin22x
a.
cos 8x
c.
cos 4x
b.
2 sin 4x
d.
mc009-1.jpg sin 16x
 

 10. 
Use identities to find the indicated value for each angle measure.
sin è =  mc010-1.jpg,   cos è > 0mc010-2.jpgFind cos(2è).
a.
mc010-3.jpg
c.
- mc010-5.jpg
b.
mc010-4.jpg
d.
mc010-6.jpg
 

 11. 
Use identities to find the indicated value for each angle measure.
tan è =  mc011-1.jpg,   ð < è < mc011-2.jpgmc011-3.jpgFind sin(2è).
a.
- mc011-4.jpg
c.
mc011-6.jpg
b.
- mc011-5.jpg
d.
mc011-7.jpg
 

 12. 
Use identities to find the indicated value for each angle measure.
tan è = mc012-1.jpg,   sin è < 0mc012-2.jpgFind cos(2è).
a.
mc012-3.jpg
c.
- mc012-5.jpg
b.
mc012-4.jpg
d.
- mc012-6.jpg
 

 13. 
Use identities to find the indicated value for each angle measure.
sin è = mc013-1.jpg,   tan è < 0mc013-2.jpgFind sin(2è).
a.
mc013-3.jpg
c.
mc013-5.jpg
b.
mc013-4.jpg
d.
- mc013-6.jpg
 

 14. 
Use identities to find the indicated value for each angle measure.
cos 2è =  mc014-1.jpgand è terminates in quadrant IIImc014-2.jpgFind cos è.
a.
cos è = 0
c.
cos è = - mc014-4.jpg
b.
cos è = - mc014-3.jpg
d.
cos è = mc014-5.jpg
 

 15. 
cos 4x
a.
cos4x - 6 sin2x cos2x + sin4x
c.
4 sin x cos3x - 4 sin3x cos x
b.
3 sin x - 4 sin3x
d.
cos3x - 3 sin2x cos x
 

 16. 
sin 3x
a.
1 - 8 sin2x cos2x
c.
4 sin x cos3x - 4 sin3x cos x
b.
3 sin x - 4 sin3x
d.
cos3x - 3 sin2x cos x
 

 17. 
Write the product as a sum or difference of trigonometric functions.
2 cos  8x cos  2x
a.
sin  10x + sin  6x
c.
cos  10x + cos  6x
b.
cos  6x - cos  10x
d.
mc017-1.jpg(cos  10x + cos  6x)
 

 18. 
Write the product as a sum or difference of trigonometric functions.
8 sin  57° cos  101°
a.
4[cos  158° + cos( -44°)]
c.
8[cos  158° + cos( -44°)]
b.
4[sin  158° + sin( -44°)]
d.
4[sin  158° - sin( -44°)]
 

 19. 
Write the product as a sum or difference of trigonometric functions.
 10 cos  26° cos  13°
a.
5(cos  39° - cos  13°)
c.
5(sin  39° - sin  13°)
b.
5(cos  39° + cos  13°)
d.
10(sin  39° + sin  13°)
 

 20. 
sin  13° - sin  44°
a.
2 cos  28.5° cos( -15.5°)
c.
2 cos  28.5° sin( -15.5°)
b.
2 sin  28.5° cos( -15.5°)
d.
2 sin  28.5° sin( -15.5°)
 

 21. 
Rewrite the following as a product of trigonometric functions.
 sin mc021-1.jpg + sin mc021-2.jpg
a.
2 sin mc021-3.jpg sin mc021-4.jpg
c.
2 cos mc021-7.jpg sin mc021-8.jpg
b.
2 cos mc021-5.jpg cos mc021-6.jpg
d.
2 sin mc021-9.jpg cos mc021-10.jpg
 

 22. 
Rewrite the following as a product of trigonometric functions.
 sin  6 + sin  38
a.
2 sin  22 sin( -16)
c.
2 cos  22 sin( -16)
b.
2 sin  22 cos( -16)
d.
2 cos  22 cos( -16)
 

 23. 
Suppose that for an electrical appliance, voltage is given by mc023-1.jpg and amperage by mc023-2.jpg where t is time in seconds. The wattage is given by mc023-3.jpg Find the maximum wattage used by the appliance.
a.
202.23
c.
101.115
b.
189
d.
404.46
 

 24. 
Suppose that a household appliance draws a current represented by the relation mc024-1.jpg where t is time measured in seconds. The power consumed by the appliance is mc024-2.jpg where R is a constant. Take R to be  16 and graph the power in mc024-3.jpg by mc024-4.jpg and use an identity to write the expression for the power in the form mc024-5.jpg where a, k, and d are constants.
a.
P = -392 cos(240ðt) +  392
[0, 0.04, 0.01] by [-200, 2000, 200]
mc024-6.jpg
b.
P =  392 cos(120ðt) +  392
[0, 0.04, 0.01] by [-200, 2000, 200]
mc024-7.jpg
c.
P =  784 cos(240ðt) +  784
[0, 0.04, 0.01] by [-200, 2000, 200]
mc024-8.jpg
d.
P =  392 cos(240ðt) +  392
[0, 0.04, 0.01] by [-200, 2000, 200]
mc024-9.jpg
 



 
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