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Trigonometric Identities and Their Significance

Trigonometric Identities and Their Significance Quiz

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Questions

Question 1 Multiple Choice (Single Answer)

What is the Pythagorean identity?

  1. sin^2(x) + cos^2(x) = 1
  2. sin(x) + cos(x) = 1
  3. tan(x) = sin(x) / cos(x)
  4. cot(x) = cos(x) / sin(x)
Question 2 Multiple Choice (Single Answer)

What is the double-angle identity for sine?

  1. sin(2x) = 2sin(x)cos(x)
  2. sin(2x) = sin(x) + sin(x)
  3. sin(2x) = sin(x) - sin(x)
  4. sin(2x) = cos(x) - cos(x)
Question 3 Multiple Choice (Single Answer)

What is the double-angle identity for cosine?

  1. cos(2x) = cos^2(x) - sin^2(x)
  2. cos(2x) = 2cos^2(x) - 1
  3. cos(2x) = 1 - 2sin^2(x)
  4. cos(2x) = 2cos(x) - 1
Question 4 Multiple Choice (Single Answer)

What is the half-angle identity for sine?

  1. sin(x/2) = sqrt((1 - cos(x))/2)
  2. sin(x/2) = sqrt((1 + cos(x))/2)
  3. sin(x/2) = (1 - cos(x))/2
  4. sin(x/2) = (1 + cos(x))/2
Question 5 Multiple Choice (Single Answer)

What is the half-angle identity for cosine?

  1. cos(x/2) = sqrt((1 + cos(x))/2)
  2. cos(x/2) = sqrt((1 - cos(x))/2)
  3. cos(x/2) = (1 + cos(x))/2
  4. cos(x/2) = (1 - cos(x))/2
Question 6 Multiple Choice (Single Answer)

What is the sum-to-product identity for sine?

  1. sin(x) + sin(y) = 2sin((x+y)/2)cos((x-y)/2)
  2. sin(x) + sin(y) = 2cos((x+y)/2)sin((x-y)/2)
  3. sin(x) - sin(y) = 2sin((x+y)/2)cos((x-y)/2)
  4. sin(x) - sin(y) = 2cos((x+y)/2)sin((x-y)/2)
Question 7 Multiple Choice (Single Answer)

What is the sum-to-product identity for cosine?

  1. cos(x) + cos(y) = 2cos((x+y)/2)cos((x-y)/2)
  2. cos(x) + cos(y) = 2sin((x+y)/2)sin((x-y)/2)
  3. cos(x) - cos(y) = 2cos((x+y)/2)cos((x-y)/2)
  4. cos(x) - cos(y) = 2sin((x+y)/2)sin((x-y)/2)
Question 8 Multiple Choice (Single Answer)

What is the product-to-sum identity for sine?

  1. sin(x)sin(y) = (cos(x-y) - cos(x+y))/2
  2. sin(x)sin(y) = (cos(x-y) + cos(x+y))/2
  3. sin(x)cos(y) = (sin(x+y) + sin(x-y))/2
  4. sin(x)cos(y) = (sin(x+y) - sin(x-y))/2
Question 9 Multiple Choice (Single Answer)

What is the product-to-sum identity for cosine?

  1. cos(x)cos(y) = (cos(x-y) + cos(x+y))/2
  2. cos(x)cos(y) = (cos(x-y) - cos(x+y))/2
  3. sin(x)cos(y) = (sin(x+y) + sin(x-y))/2
  4. sin(x)cos(y) = (sin(x+y) - sin(x-y))/2
Question 10 Multiple Choice (Single Answer)

What is the addition formula for sine?

  1. sin(x + y) = sin(x)cos(y) + cos(x)sin(y)
  2. sin(x + y) = sin(x)cos(y) - cos(x)sin(y)
  3. sin(x - y) = sin(x)cos(y) + cos(x)sin(y)
  4. sin(x - y) = sin(x)cos(y) - cos(x)sin(y)
Question 11 Multiple Choice (Single Answer)

What is the addition formula for cosine?

  1. cos(x + y) = cos(x)cos(y) - sin(x)sin(y)
  2. cos(x + y) = cos(x)cos(y) + sin(x)sin(y)
  3. cos(x - y) = cos(x)cos(y) - sin(x)sin(y)
  4. cos(x - y) = cos(x)cos(y) + sin(x)sin(y)
Question 12 Multiple Choice (Single Answer)

What is the subtraction formula for sine?

  1. sin(x - y) = sin(x)cos(y) - cos(x)sin(y)
  2. sin(x - y) = sin(x)cos(y) + cos(x)sin(y)
  3. cos(x - y) = cos(x)cos(y) - sin(x)sin(y)
  4. cos(x - y) = cos(x)cos(y) + sin(x)sin(y)
Question 13 Multiple Choice (Single Answer)

What is the subtraction formula for cosine?

  1. cos(x - y) = cos(x)cos(y) + sin(x)sin(y)
  2. cos(x - y) = cos(x)cos(y) - sin(x)sin(y)
  3. sin(x + y) = sin(x)cos(y) + cos(x)sin(y)
  4. sin(x + y) = sin(x)cos(y) - cos(x)sin(y)
Question 14 Multiple Choice (Single Answer)

What is the double-angle formula for sine?

  1. sin(2x) = 2sin(x)cos(x)
  2. sin(2x) = sin(x) + sin(x)
  3. sin(2x) = sin(x) - sin(x)
  4. sin(2x) = cos(x) - cos(x)
Question 15 Multiple Choice (Single Answer)

What is the double-angle formula for cosine?

  1. cos(2x) = cos^2(x) - sin^2(x)
  2. cos(2x) = 2cos^2(x) - 1
  3. cos(2x) = 1 - 2sin^2(x)
  4. cos(2x) = 2cos(x) - 1
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