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MATH1720HomeworkChapter5Section1

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

 1. 
Use the fundamental identities to find the value of the trigonometric function.
Find sin è if cos è = mc001-1.jpg and è is in quadrant IV.
a.
- mc001-2.jpg
c.
mc001-4.jpg
b.
- mc001-3.jpg
d.
mc001-5.jpg
 

 2. 
Use the fundamental identities to find the value of the trigonometric function.
Find csc è if sin è = - mc002-1.jpg and è is in quadrant IV.
a.
- mc002-2.jpg
c.
mc002-4.jpg
b.
- mc002-3.jpg
d.
mc002-5.jpg
 

 3. 
Use the fundamental identities to find the value of the trigonometric function.
Find tan è if sin è = mc003-1.jpg and è is in quadrant II.
a.
mc003-2.jpg
c.
- mc003-4.jpg
b.
- mc003-3.jpg
d.
- mc003-5.jpg
 

 4. 
Use the fundamental identities to find the value of the trigonometric function.
Find sec è if tan è = mc004-1.jpg and è is in quadrant I.
a.
- mc004-2.jpg
c.
mc004-4.jpg
b.
mc004-3.jpg
d.
- mc004-5.jpg
 

 5. 
Use the fundamental identities to find the value of the trigonometric function.
Find cot è if tan è = mc005-1.jpg and è is in quadrant III.
a.
- mc005-2.jpg
c.
- mc005-4.jpg
b.
mc005-3.jpg
d.
mc005-5.jpg
 

 6. 
Use the fundamental identities to find the value of the trigonometric function.
 Find cos è if tan è = mc006-1.jpg and è is in quadrant III.
a.
- mc006-2.jpg
c.
- mc006-4.jpg
b.
mc006-3.jpg
d.
mc006-5.jpg
 

 7. 
Use the fundamental identities to find the value of the trigonometric function.
Find cos è if csc è = - mc007-1.jpg and è is in quadrant IV.
a.
mc007-2.jpg
c.
mc007-4.jpg
b.
mc007-3.jpg
d.
- mc007-5.jpg
 

 8. 
Use the fundamental identities to find the value of the trigonometric function.
Find sin è if cos è = mc008-1.jpg and è is in quadrant IV.
a.
mc008-2.jpg
c.
mc008-4.jpg
b.
- mc008-3.jpg
d.
mc008-5.jpg
 

 9. 
Use the fundamental identities to find the value of the trigonometric function.
Find sin è if cos è = - mc009-1.jpg and è is in quadrant III.
a.
- mc009-2.jpg
c.
- mc009-4.jpg
b.
- mc009-3.jpg
d.
mc009-5.jpg
 

 10. 
Use the fundamental identities to find the value of the trigonometric function.
Find cos è if sin è = - mc010-1.jpg and è is in quadrant III.
a.
mc010-2.jpg
c.
- mc010-4.jpg
b.
- mc010-3.jpg
d.
- mc010-5.jpg
 

 11. 
Use the fundamental identities to find the value of the trigonometric function.
 Find tan è if cos è = mc011-1.jpg and è is in quadrant IV.
a.
- mc011-2.jpg
c.
- mc011-3.jpg
b.
2
d.
- mc011-4.jpg
 

 12. 
Use the fundamental identities to find the value of the trigonometric function.
Find csc è if cot è = - mc012-1.jpg and è is in quadrant II.
a.
mc012-2.jpg
c.
4
b.
-  4
d.
- mc012-3.jpg
 

 13. 
Use the fundamental identities to find the value of the trigonometric function.
Find cot è if csc è = mc013-1.jpg and è is in quadrant I.
a.
mc013-2.jpg
c.
3
b.
mc013-3.jpg
d.
mc013-4.jpg
 

 14. 
Use the fundamental identities to find the value of the trigonometric function.
Find sec è if cos è = mc014-1.jpg and sin è > 0.
a.
mc014-2.jpg
c.
-  4
b.
mc014-3.jpg
d.
4
 

 15. 
For the graph of a circular function y = f(x), determine whether f(-x) = f(x) or f(-x) = -f(x) is true.
mc015-1.jpg
a.
f(-x) = -f(x)
b.
f(-x) = f(x)
 

 16. 
For the graph of a circular function y = f(x), determine whether f(-x) = f(x) or f(-x) = -f(x) is true.
mc016-1.jpg
a.
f(-x) = f(x)
b.
f(-x) = -f(x)
 

 17. 
For the graph of a circular function y = f(x), determine whether f(-x) = f(x) or f(-x) = -f(x) is true.
mc017-1.jpg
a.
f(-x) = -f(x)
b.
f(-x) = f(x)
 

 18. 
For the graph of a circular function y = f(x), determine whether f(-x) = f(x) or f(-x) = -f(x) is true.
mc018-1.jpg
a.
f(-x) = -f(x)
b.
f(-x) = f(x)
 

 19. 
For the graph of a circular function y = f(x), determine whether f(-x) = f(x) or f(-x) = -f(x) is true.
mc019-1.jpg
a.
f(-x) = -f(x)
b.
f(-x) = f(x)
 

 20. 
For the graph of a circular function y = f(x), determine whether f(-x) = f(x) or f(-x) = -f(x) is true.
mc020-1.jpg
a.
f(-x) = f(x)
b.
f(-x) = -f(x)
 

 21. 
Complete the sentence so the result is an identity. Let x be any real number.
     + sin2x = 1
a.
csc2x
c.
cos2x
b.
sin2x
d.
tan2x
 

 22. 
Complete the sentence so the result is an identity. Let x be any real number.
      + tan2x = sec2x
a.
-1
c.
cos2x
b.
1
d.
sin2x
 

 23. 
Complete the sentence so the result is an identity. Let x be any real number.
 1 +      = csc2x
a.
cot2x
c.
sec2x
b.
sin2x
d.
cos2x
 

 24. 
Complete the sentence so the result is an identity. Let x be any real number.
 1 -      = sin2x
a.
sec2x
c.
cos2x
b.
tan2x
d.
cot2x
 

 25. 
Complete the sentence so the result is an identity. Let x be any real number.
      - 1 = tan2x
a.
sec2x
c.
sin2x
b.
cos2x
d.
cot2x
 

 26. 
Complete the sentence so the result is an identity. Let x be any real number.
     = mc026-1.jpg
a.
tan x
c.
cot x
b.
csc x
d.
sec x
 

 27. 
Complete the sentence so the result is an identity. Let x be any real number.
mc027-1.jpg = mc027-2.jpg
a.
cos x
c.
sec x
b.
cot x
d.
csc x
 

 28. 
Complete the sentence so the result is an identity. Let x be any real number.
 sin x = (     )(cos x)
a.
csc x
c.
tan x
b.
sec x
d.
cot x
 

 29. 
Complete the sentence so the result is an identity. Let x be any real number.
 cos x = (cot x)(     )
a.
sec x
c.
csc x
b.
sin x
d.
tan x
 

 30. 
Perform the transformation.
Write  sec x in terms of  sin x.
a.
± mc030-1.jpg
c.
mc030-3.jpg
b.
mc030-2.jpg
d.
mc030-4.jpg
 

 31. 
Perform the transformation.
Write  cos x in terms of  cot x.
a.
± mc031-1.jpg
c.
mc031-3.jpg
b.
mc031-2.jpg
d.
mc031-4.jpg
 

 32. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
 (1 + cot è)(1 - cot è) - mc032-1.jpg è
a.
2
c.
2 mc032-3.jpg è
b.
-2 mc032-2.jpg è
d.
0
 

 33. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
csc x(sin x + cos x)
a.
sin x tan x
c.
sec x csc x
b.
-2 tan2 x
d.
1 + cot x
 

 34. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
tan x(cot x - cos x)
a.
1 - sin x
c.
0
b.
- sec2 x
d.
1
 

 35. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
sin2 x + sin2 x cot2 x
a.
cot2 x + 1
c.
sin2 x + 1
b.
cot2 x - 1
d.
1
 

 36. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
mc036-1.jpg
a.
csc2 x
c.
cot2 x
b.
sec2 x
d.
1
 

 37. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
mc037-1.jpg
a.
sin è
c.
cos3è
b.
tan2è
d.
sec2è
 

 38. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
tan2è csc2è
a.
cos3è
c.
tan2è
b.
sin è
d.
sec2è
 

 39. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
sin2 x(cot2 x + 1)
a.
cos2 x + 1
c.
tan2 x
b.
-1
d.
1
 

 40. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
 mc040-1.jpg
a.
csc x
c.
1
b.
-sec x
d.
sec x
 

 41. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
mc041-1.jpg
a.
-sin x
c.
sin x
b.
cos x
d.
-cos x
 

 42. 
Use a graphing calculator to make a conjecture as to whether each equation is an identity.
 cos 2x = sin 2x tan x
a.
Not an identity
b.
Identity
 

 43. 
Use a graphing calculator to make a conjecture as to whether each equation is an identity.
 sin 2x = 2sin x cos x
a.
Identity
b.
Not an Identity
 

 44. 
Use a graphing calculator to make a conjecture as to whether each equation is an identity.
 (sin x + cos x)2 = 1
a.
Not an identity
b.
Identity
 

 45. 
Use a graphing calculator to make a conjecture as to whether each equation is an identity.
sin mc045-1.jpg cos mc045-2.jpg = mc045-3.jpg
a.
Not an identity
b.
Identity
 

 46. 
Use a graphing calculator to make a conjecture as to whether each equation is an identity.
 sin 2x = 2 sin x
a.
Identity
b.
Not an identity
 

 47. 
Use a graphing calculator to make a conjecture as to whether each equation is an identity.
cos 2x = 2mc047-1.jpgx - 1
a.
Not an Identity
b.
Identity
 

 48. 
Use a graphing calculator to make a conjecture as to whether each equation is an identity.
cos(x + y) = cos x + cos y
a.
Identity
b.
Not an Identity
 



 
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