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MATH1720HomeworkChapter5Section2

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

 1. 
Perform the indicated operations and simplify the result so there are no quotients.
sec è - mc001-1.jpg
a.
sec è csc è
c.
sin è tan è
b.
-2 tan2è
d.
1 + cot è
 

 2. 
Perform the indicated operations and simplify the result so there are no quotients.
csc è(sin è + cos è)
a.
1 + cot è
c.
sin è tan è
b.
sec è csc è
d.
-2 tan2è
 

 3. 
Perform the indicated operations and simplify the result so there are no quotients.
mc003-1.jpg - mc003-2.jpg
a.
sec è csc è
c.
1 + cot è
b.
-2 tan2è
d.
sin è tan è
 

 4. 
Perform the indicated operations and simplify the result so there are no quotients.
mc004-1.jpg + mc004-2.jpg
a.
sec è csc è
c.
sin è tan è
b.
-2 tan2è
d.
1 + cot è
 

 5. 
Perform the indicated operations and simplify the result so there are no quotients.
 tan2è - 3 sin è tan è sec è
a.
sin è tan è
c.
-2 tan2è
b.
1 + cot è
d.
sec è csc è
 

 6. 
Perform the indicated operations and simplify the result so there are no quotients.
mc006-1.jpg
a.
1
c.
0
b.
1 - sin è
d.
- sec2è
 

 7. 
Perform the indicated operations and simplify the result so there are no quotients.
mc007-1.jpg - mc007-2.jpg
a.
0
c.
1
b.
- sec2è
d.
1 - sin è
 

 8. 
Perform the indicated operations and simplify the result so there are no quotients.
2 tan è - (1 + tan è)2
a.
- sec2è
c.
1 - sin è
b.
0
d.
1
 

 9. 
Perform the indicated operations and simplify the result so there are no quotients.
 tan è(cot è - cos è)
a.
0
c.
- sec2è
b.
1 - sin è
d.
1
 

 10. 
Perform the indicated operations and simplify the result so there are no quotients.
 mc010-1.jpg - 1
a.
0
c.
1 - sin è
b.
- sec2è
d.
1
 

 11. 
Factor the trigonometric expression and simplify.
1 - 2 sin2x + sin4x
a.
cos4x
c.
(1 + tan2x)
b.
sin2x
d.
(1 - sin2x)
 

 12. 
Factor the trigonometric expression and simplify.
sec4x - 2 sec2x tan2x + tan4x
a.
sec2x (1 + tan2x)
c.
sec2x + tan2x
b.
2
d.
1
 

 13. 
Factor the trigonometric expression and simplify.
 sin2x + sin2x cot2x
a.
sin2x + 1
c.
cot2x + 1
b.
cot2x - 1
d.
1
 

 14. 
Factor the trigonometric expression and simplify.
sec4x + sec2x tan2x - 2 tan4x
a.
4 sec2x
c.
sec2x + 2
b.
tan2x - 1
d.
3 sec2x - 2
 

 15. 
Factor the trigonometric expression and simplify.
1 - sin3x
a.
(1- sin x)(cos x + sin2x)
c.
(1 - sin x)(1 - 2 sin x + sin2x)
b.
(1- sin x)(1 + sin x + sin2x)
d.
(1 - sin x)3
 

 16. 
Factor the trigonometric expression and simplify.
 tan4x - sec4x
a.
-2 tan2x - 1
c.
sec2x + tan2x
b.
sec2x
d.
tan 2 - sec2x
 

 17. 
Use the fundamental identities to simplify the expression.
mc017-1.jpg
a.
csc2è
c.
sec2è
b.
1
d.
cot2è
 

 18. 
Use the fundamental identities to simplify the expression.
 mc018-1.jpg + csc è sin è
a.
1
c.
csc2è
b.
sec2è
d.
tan2è
 

 19. 
Use the fundamental identities to simplify the expression.
mc019-1.jpg + sec è cos è
a.
sec2è
c.
tan2è
b.
1
d.
csc2è
 

 20. 
Use the fundamental identities to simplify the expression.
cos è - cos è sin2è
a.
sec2è
c.
sin è
b.
cos3è
d.
tan2è
 

 21. 
Use the fundamental identities to simplify the expression.
mc021-1.jpg
a.
tan2è
c.
cos3è
b.
sin è
d.
sec2è
 

 22. 
Use the fundamental identities to simplify the expression.
sin2è + tan2è + cos2è
a.
cos3è
c.
sec2è
b.
sin è
d.
tan2è
 

 23. 
Use the fundamental identities to simplify the expression.
 mc023-1.jpg
a.
sec2è
c.
cos3è
b.
sin è
d.
tan2è
 

 24. 
Use the fundamental identities to simplify the expression.
 tan2è csc2è
a.
sec2è
c.
sin è
b.
cos3è
d.
tan2è
 

 25. 
Use the fundamental identities to simplify the expression.
1 - mc025-1.jpg è
a.
- mc025-2.jpg è
c.
mc025-4.jpg è
b.
mc025-3.jpg è
d.
cos è
 

 26. 
Use the fundamental identities to simplify the expression.
1 - mc026-1.jpg è
a.
mc026-2.jpg è
c.
mc026-4.jpg è
b.
- mc026-3.jpg è
d.
sin è
 

 27. 
Use the fundamental identities to simplify the expression.
cot è sec è sin è
a.
csc2è
c.
sec2è
b.
1
d.
tan2è
 

 28. 
Use the fundamental identities to simplify the expression.
sin è cos è sec è csc è
a.
sec2è
c.
1
b.
csc2è
d.
tan2è
 

 29. 
Use the fundamental identities to simplify the expression.
 cos (-x) cos x - sin (-x) sin x
a.
cos2x sin2x
c.
1
b.
2
d.
0
 

 30. 
Use the fundamental identities to simplify the expression.
cos x (csc x - sec x) - cot x
a.
0
c.
cos2x - tan2x
b.
-1
d.
1
 

 31. 
Use the fundamental identities to simplify the expression.
 cos x tan x
a.
cos x
c.
1
b.
cot x
d.
sin x
 

 32. 
Use the fundamental identities to simplify the expression.
mc032-1.jpg
a.
sin x
c.
sin2 x
b.
cos x
d.
cos2 x
 

 33. 
Use the fundamental identities to simplify the expression.
mc033-1.jpg
a.
1
c.
csc x
b.
-sec x
d.
sec x
 

 34. 
Use the fundamental identities to simplify the expression.
mc034-1.jpg - tan x
a.
cot x
c.
tan x
b.
csc x
d.
tan2 x
 

 35. 
Use the fundamental identities to simplify the expression.
mc035-1.jpg + cos x sec x
a.
csc2 x
c.
sec2 x
b.
csc x
d.
cot2 x
 

 36. 
Use the fundamental identities to simplify the expression.
sin2 x(cot2 x + 1)
a.
-1
c.
cos2 x + 1
b.
1
d.
tan2 x
 

 37. 
Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
 cot x cos x + sin x = csc x
a.
Identity
b.
Not an Identity
 

 38. 
Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
 (csc è + cot è)(1 - cos è) = sin è
a.
Not an Identity
b.
Identity
 

 39. 
Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
mc039-1.jpg = tan è
a.
Identity
b.
Not an Identity
 

 40. 
Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
 mc040-1.jpg + mc040-2.jpg = mc040-3.jpg x
a.
Not an Identity
b.
Identity
 

 41. 
Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
mc041-1.jpg = 4csc x + 7sec x
a.
Identity
b.
Not an Identity
 

 42. 
Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
 (cos è + cot è)(1 - csc è) = mc042-1.jpg è
a.
Not an Identity
b.
Identity
 

 43. 
Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
mc043-1.jpg = sin x
a.
Identity
b.
Not an identity
 

 44. 
Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
 mc044-1.jpg = sin x
a.
Not an identity
b.
Identity
 

 45. 
Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
mc045-1.jpg = 1
a.
Not an identity
b.
Identity
 

 46. 
The power dissipated in an electric circuit is given by the expression mc046-1.jpg where R is the resistance of the circuit and I is the current through the circuit. For a sinusoidal alternating current, the current might be represented by the relation mc046-2.jpg where A is the amplitude, f is the frequency, and t is time. Write an expression for P involving the sine function, and use a fundamental identity to write P in terms of the cosine function.
a.
P = RA mc046-3.jpg(2ðft) ;  P = RA - mc046-4.jpg(2ðft)
b.
P = RA mc046-5.jpg(2ðft) ;  P = RA - RA mc046-6.jpg(2ðft)
c.
P = Rmc046-7.jpg mc046-8.jpg(2ðft) ;  P = - Rmc046-9.jpg mc046-10.jpg(2ðft)
d.
P = Rmc046-11.jpg mc046-12.jpg(2ðft) ;  P = Rmc046-13.jpg - Rmc046-14.jpg mc046-15.jpg(2ðft)
 



 
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