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Trigonometric Identities

This quiz is designed to assess your understanding of trigonometric identities. Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables involved. These identities are useful in solving a variety of trigonometric problems.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is an identity?

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

What is the reciprocal identity for sine?

  1. sin(x) = 1/csc(x)
  2. sin(x) = 1/sec(x)
  3. sin(x) = 1/tan(x)
  4. sin(x) = 1/cot(x)
Question 3 Multiple Choice (Single Answer)

Which of the following is the quotient identity for tangent?

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

Which of the following 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 6 Multiple Choice (Single Answer)

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

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

Which of the following is the difference-to-product identity for sine and cosine?

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

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

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

Which of the following is the product-to-sum identity for cosine and sine?

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

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

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

Which of the following is the difference-to-product identity for tangent?

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

What is the half-angle identity for tangent?

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

Which of the following is the double-angle identity for tangent?

  1. tan(2x) = (2tan(x))/(1 - tan^2(x))
  2. tan(2x) = (2tan(x))/(1 + tan^2(x))
  3. tan(2x) = (tan(x))/(1 - tan^2(x))
  4. tan(2x) = (tan(x))/(1 + tan^2(x))
Question 14 Multiple Choice (Single Answer)

What is the power-reducing identity for sine?

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

Which of the following is the power-reducing identity for cosine?

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