Trigonometry Identities and Anti-Derivatives

Joel Riggs
Quiz by Joel Riggs, updated more than 1 year ago
Joel Riggs
Created by Joel Riggs over 5 years ago
31
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Trigonometry Identities and Anti-Derivatives

Resource summary

Question 1

Question
What is the antiderivative of csc²(kx)?
Answer
  • -(1/k)cot(kx)+c
  • (1/k)cot(kx)+c
  • -(1/k)tangent(kx)+c
  • (1/k)tangent(kx)+c
  • (1/k)sec(kx)+c
  • -(1/k)sec(kx)+c

Question 2

Question
What is the antiderivative of sec²(x)?
Answer
  • (1/k)tangent(kx)+c
  • -(1/k)tangent(kx)+c
  • -(1/k)csc(kx)+c
  • (1/k)csc(kx)+c
  • -(1/k)sin(kx)+c
  • (1/k)sin(kx)+c

Question 3

Question
Which is an identity of sin²(x)?
Answer
  • (1-cos(2x))*(1/2)
  • (1+cos(2x))*(1/2)
  • cos(x)
  • sin(x)cos(y)+cos(x)sin(y)
  • 2tan(x)/(1-tan²(x))
  • 2sin((x+y)/2)sin((x-y)/2)

Question 4

Question
Which of the following are identities of tan²(x)?
Answer
  • (1-cos(2x))/(1+cos(2x))
  • (1+cos(2x))/(1-cos(2x))
  • [tangent(x)+tangent(y)]/[1-tangent(x)tangent(y)]
  • (1/2)*[cos(x+y)+cos(x-y)]

Question 5

Question
What is the antiderivative of csc(kx)cot(kx)?
Answer
  • -(1/k)csc(kx)+c
  • (1/k)csc(kx)+c
  • (1/k)[sin(kx)/cos(kx)]+c
  • -(1/k)[sin(kx)/cos(kx)]+c

Question 6

Question
What is the antiderivative of sec(kx)tangent(kx)?
Answer
  • (1/k)sec(kx)+c
  • -(1/k)sec(kx)+c
  • (1/k)csc(kx)+c
  • -(1/k)csc(kx)+c

Question 7

Question
What is the anti-derivative of sin(kx)
Answer
  • -(1/k)cos(kx)+c
  • (1/k)cos(kx)+c
  • (1/k)sin(kx)+c
  • (1/k)csc(kx)+c

Question 8

Question
Which of the following are identities of cos(2x)?
Answer
  • cos²(x)-sin²(x)
  • 1-2sin²(x)
  • 2cos²(x)-1
  • 2cos²(x)+1
  • (1-cos(2x))*(1/2)
  • csc²(x)
  • cos(x)cos(y)+sin(x)sin(y)
  • (1-cos(2x))/(1+cos(2x))
  • 2/(cot(x)-tangent(x))

Question 9

Question
What is the anti-derivative of cos(kx)
Answer
  • (1/k)sin(kx)+c
  • -(1/k)sin(kx)+c
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