Gr 11 Math Ch 6: Trigonometric Identities

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What is the definition of the quotient identity?

tan θ = sin θ / cos θ for all values of θ, except where sin θ = 0 and cos θ ≠ 0

tan θ = sin θ / cos θ for all values of θ

tan θ = sin θ / cos θ for all values of θ, except where sin θ = 0

tan θ = cos θ / sin θ for all values of θ, except where cos θ = 0 (correct)

What is the square identity in trigonometry?

sin θ + cos θ = 1

sin θ × cos θ = 1

sin θ - cos θ = 1

sin² θ + cos² θ = 1 (correct)

Why do we replace 1 with sin² θ + cos² θ in trigonometric expressions?

To eliminate sine and cosine terms

To simplify the expression (correct)

To make the expression more complex

To introduce a quotient identity

What is the purpose of the square root sign in trigonometric expressions?

To indicate the use of a square identity Signup and view all the answers

How can we express the square identity in an alternative form?

sin² θ = 1 - cos² θ Signup and view all the answers

Why do we multiply by a suitable fraction in trigonometric expressions?

To simplify the expression Signup and view all the answers

What is the purpose of trigonometric identities?

To simplify expressions containing sine and cosine ratios Signup and view all the answers

What is the quotient identity for tangent in terms of sine and cosine?

tan θ = sin θ / cos θ Signup and view all the answers

When is tan θ undefined?

When cos θ = 0 Signup and view all the answers

What is the square identity, also known as the Pythagorean identity?

sin² θ + cos² θ = 1 Signup and view all the answers

Which of the following is a useful tip for proving identities?

Change all trigonometric ratios to sine and cosine Signup and view all the answers

What is an alternative form of the square identity?

sin² θ = 1 - cos² θ Signup and view all the answers

How can the sine and cosine functions be written in terms of x, y, and r?

sin θ = y/r and cos θ = x/r Signup and view all the answers

What is the reason for the quotient identity being derived using a right-angled triangle?

Because it allows us to use the Pythagorean theorem Signup and view all the answers

What is the purpose of replacing 1 with sin²θ + cos²θ in trigonometric expressions?

To simplify the expressions Signup and view all the answers

When proving trigonometric identities, why do we often need to simplify both sides of the equation?

To show that they are equal Signup and view all the answers

What is the advantage of expressing the square identity in alternative forms?

It provides more ways to simplify trigonometric expressions Signup and view all the answers

Why do we multiply by a suitable fraction in trigonometric expressions?

To simplify the expressions Signup and view all the answers

What is the relationship between sin²θ and cos²θ in the square identity?

sin²θ + cos²θ = 1 Signup and view all the answers

What is the trigonometric function that can be expressed as the ratio of sine to cosine?

tan θ Signup and view all the answers

What is the purpose of expressing trigonometric expressions in terms of sine and cosine ratios only?

To simplify a given expression Signup and view all the answers

Which of the following is true about the tangent function?

It is undefined if cos θ = 0 Signup and view all the answers

What is the result of using the Pythagorean theorem to write the sine and cosine functions in terms of x, y, and r?

sin² θ + cos² θ = 1 Signup and view all the answers

What is a common approach when proving trigonometric identities?

Choosing one side of the equation to simplify and show that it is equal to the other side Signup and view all the answers

Why is it necessary to express trigonometric expressions in terms of sine and cosine ratios only?

All of the above Signup and view all the answers

What is the relationship between the sine and cosine functions in the square identity?

sin² θ + cos² θ = 1 Signup and view all the answers

What is the result of deriving the tangent function using a right-angled triangle?

tan θ = sin θ / cos θ Signup and view all the answers

What is the purpose of changing all trigonometric ratios to sine and cosine?

To facilitate the proof of identities Signup and view all the answers

What is the primary reason for using the quotient identity when simplifying trigonometric expressions?

To express the tangent function in terms of sine and cosine ratios only Signup and view all the answers

When proving trigonometric identities, why is it often necessary to add or multiply both sides of the equation by a suitable expression?

To simplify the expression and make it more manageable Signup and view all the answers

What is the main advantage of expressing the square identity in alternative forms?

It simplifies the process of proving trigonometric identities Signup and view all the answers

When is it necessary to replace 1 with sin²θ + cos²θ in a trigonometric expression?

When the expression can be simplified using the square identity Signup and view all the answers

What is the primary purpose of using the quotient identity in trigonometric proofs?

To express the tangent function in terms of sine and cosine ratios Signup and view all the answers

What is the main advantage of using the square identity in trigonometric expressions?

It simplifies the process of proving trigonometric identities by eliminating variables Signup and view all the answers

What is the primary reason for expressing trigonometric expressions in terms of sine and cosine ratios only?

To enable proof of other identities and solve equations Signup and view all the answers

Which of the following statements is true about the quotient identity?

It is derived using the Pythagorean theorem Signup and view all the answers

What is the main advantage of using alternative forms of the square identity?

It enables the proof of other identities and solution of equations Signup and view all the answers

Which of the following is a common pitfall when proving trigonometric identities?

Not simplifying both sides of the equation Signup and view all the answers

What is the primary purpose of the quotient identity in trigonometry?

To prove other identities and solve equations Signup and view all the answers

Which of the following is a consequence of the square identity?

The square of sine plus the square of cosine is always equal to 1 Signup and view all the answers

What is the primary reason for using the Pythagorean theorem in trigonometry?

To derive the quotient identity Signup and view all the answers

Which of the following is a common approach when proving trigonometric identities?

Simplifying both sides of the equation and showing that they are equal Signup and view all the answers

Gr 11 Math Ch 6: Trigonometric Identities

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Questions and Answers

What is the definition of the quotient identity?

What is the square identity in trigonometry?

Why do we replace 1 with sin² θ + cos² θ in trigonometric expressions?

What is the purpose of the square root sign in trigonometric expressions?

How can we express the square identity in an alternative form?

Why do we multiply by a suitable fraction in trigonometric expressions?

What is the purpose of trigonometric identities?

What is the quotient identity for tangent in terms of sine and cosine?

When is tan θ undefined?

What is the square identity, also known as the Pythagorean identity?

Which of the following is a useful tip for proving identities?

What is an alternative form of the square identity?

How can the sine and cosine functions be written in terms of x, y, and r?

What is the reason for the quotient identity being derived using a right-angled triangle?

What is the purpose of replacing 1 with sin²θ + cos²θ in trigonometric expressions?

When proving trigonometric identities, why do we often need to simplify both sides of the equation?

What is the advantage of expressing the square identity in alternative forms?

Why do we multiply by a suitable fraction in trigonometric expressions?

What is the relationship between sin²θ and cos²θ in the square identity?

What is the trigonometric function that can be expressed as the ratio of sine to cosine?

What is the purpose of expressing trigonometric expressions in terms of sine and cosine ratios only?

Which of the following is true about the tangent function?

What is the result of using the Pythagorean theorem to write the sine and cosine functions in terms of x, y, and r?

What is a common approach when proving trigonometric identities?

Why is it necessary to express trigonometric expressions in terms of sine and cosine ratios only?

What is the relationship between the sine and cosine functions in the square identity?

What is the result of deriving the tangent function using a right-angled triangle?

What is the purpose of changing all trigonometric ratios to sine and cosine?

What is the primary reason for using the quotient identity when simplifying trigonometric expressions?

When proving trigonometric identities, why is it often necessary to add or multiply both sides of the equation by a suitable expression?

What is the main advantage of expressing the square identity in alternative forms?

When is it necessary to replace 1 with sin²θ + cos²θ in a trigonometric expression?

What is the primary purpose of using the quotient identity in trigonometric proofs?

What is the main advantage of using the square identity in trigonometric expressions?

What is the primary reason for expressing trigonometric expressions in terms of sine and cosine ratios only?

Which of the following statements is true about the quotient identity?

What is the main advantage of using alternative forms of the square identity?

Which of the following is a common pitfall when proving trigonometric identities?

What is the primary purpose of the quotient identity in trigonometry?

Which of the following is a consequence of the square identity?

What is the primary reason for using the Pythagorean theorem in trigonometry?

Which of the following is a common approach when proving trigonometric identities?

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