Gr 11 Math Ch 6: Reduction Formula
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Questions and Answers

What is the value of sin(180° - θ) in terms of θ?

  • sin θ (correct)
  • -sin θ
  • -cos θ
  • cos θ

    • What is the value of cos(180° + θ) in terms of θ?

  • cos θ
  • -sin θ
  • sin θ
  • -cos θ (correct)

    • What is the value of tan(180° - θ) in terms of θ?

  • -tan θ (correct)
  • tan θ
  • -cot θ
  • cot θ

    • What is the coordinate of point P' in terms of point P(√3, 1), given P and P' are symmetrical about the y-axis?

    <p>(-√3, 1)</p> Signup and view all the answers

    If OP makes an angle θ = 30° with the x-axis, what is the value of θ for point P'(180° + θ)?

    <p>120°</p> Signup and view all the answers

    What is the value of sin(180° + θ) in terms of θ?

    <p>-sin θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the origin, what are the coordinates of P' if P has coordinates (√3, 1)?

    <p>(-√3, -1)</p> Signup and view all the answers

    What is the value of sin(180° + θ)?

    <p>-sin θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the x-axis, what are the coordinates of P' if P has coordinates (√3, 1)?

    <p>(√3, -1)</p> Signup and view all the answers

    What is the value of cos(-θ)?

    <p>cos θ</p> Signup and view all the answers

    What is the value of tan(360° - θ)?

    <p>-tan θ</p> Signup and view all the answers

    What is the value of sin(90° - θ)?

    <p>cos θ</p> Signup and view all the answers

    What is the value of cos(90° + θ)?

    <p>-sin θ</p> Signup and view all the answers

    What is the value of tan(90° + θ)?

    <p>tan θ</p> Signup and view all the answers

    Express sin 54° as a trigonometric ratio of 36°:

    <p>cos 36°</p> Signup and view all the answers

    What is the phase difference between the sine and cosine graphs?

    <p>90°</p> Signup and view all the answers

    If point P has coordinates (√3, 1) and point P' is symmetrical about the y-axis, what are the coordinates of P'?

    <p>(-√3, 1)</p> Signup and view all the answers

    What is the value of cos(180° + θ) in terms of θ?

    <p>-cos θ</p> Signup and view all the answers

    What is the value of tan(180° - θ) in terms of tan θ?

    <p>-tan θ</p> Signup and view all the answers

    What is the relationship between the coordinates of points P and P' when they are symmetrical about the y-axis?

    <p>P' has coordinates (-x, y) if P has coordinates (x, y)</p> Signup and view all the answers

    What is the value of sin(180° - θ) in terms of sin θ?

    <p>sin θ</p> Signup and view all the answers

    What is the relationship between the coordinates of points P and P' when they are symmetrical about the origin?

    <p>P' has coordinates (-x, -y) if P has coordinates (x, y)</p> Signup and view all the answers

    If points P and P' are symmetrical about the origin, which of the following is true about P'?

    <p>P' has coordinates (-x, -y).</p> Signup and view all the answers

    What is the value of sin(360° + θ) in terms of θ?

    <p>sin θ</p> Signup and view all the answers

    If P and P' are symmetrical about the line y = x, what are the coordinates of P'?

    <p>(y, x)</p> Signup and view all the answers

    What is the value of cos(-θ) in terms of θ?

    <p>cos θ</p> Signup and view all the answers

    What is the value of tan(180° - θ) in terms of θ?

    <p>-tan θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the x-axis, what are the coordinates of P'?

    <p>(x, -y)</p> Signup and view all the answers

    What is the value of cos(360° - θ) in terms of θ?

    <p>cos θ</p> Signup and view all the answers

    What is the value of sin(90° + θ) in terms of θ?

    <p>cos θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what are the coordinates of P'?

    <p>(-x, y)</p> Signup and view all the answers

    What is the value of tan(180° + θ) in terms of θ?

    <p>tan θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, which of the following is true about the tangent of the angle?

    <p>tan(180^\circ - ) = -tan</p> Signup and view all the answers

    What is the relationship between the sine and cosine of 180^\circ - and ?

    <p>sin(180^\circ - ) = sin , cos(180^\circ - ) = -cos</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what is the relationship between the coordinates of P and P'?

    <p>P'(-x, y)</p> Signup and view all the answers

    What is the value of cos(180^\circ - ) in terms of ?

    <p>-cos</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what is the value of sin(180^\circ - ) in terms of ?

    <p>sin</p> Signup and view all the answers

    What is the value of tan(180^\circ - ) in terms of ?

    <p>-tan</p> Signup and view all the answers

    If points P and P' are symmetrical about the line y = x, what is the value of tan(90° + θ) in terms of θ?

    <p>-tan θ</p> Signup and view all the answers

    What is the value of sin(360° - θ) in terms of θ, if 0° ≤ θ ≤ 360°?

    <p>-sin θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the x-axis, what is the value of cos(90° - θ) in terms of θ?

    <p>sin θ</p> Signup and view all the answers

    What is the value of tan(-θ) in terms of θ?

    <p>-tan θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the origin, what is the value of cos(180° + θ) in terms of θ?

    <p>-cos θ</p> Signup and view all the answers

    What is the value of sin(360° + θ) in terms of θ, if 0° ≤ θ ≤ 360°?

    <p>sin θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the line y = x, what is the value of sin(90° + θ) in terms of θ?

    <p>cos θ</p> Signup and view all the answers

    What is the value of cos(180° - θ) in terms of θ?

    <p>-cos θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what is the value of tan(90° - θ) in terms of θ?

    <p>cot θ</p> Signup and view all the answers

    What is the value of sin(-θ) in terms of θ?

    <p>-sin θ</p> Signup and view all the answers

    What is the value of cos(360° - θ) in terms of θ, if 0° ≤ θ ≤ 360°?

    <p>cos θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what is the relationship between the sine of the angle of P and P'?

    <p>sin(180° - θ) = sin θ</p> Signup and view all the answers

    What is the value of tan(360° - θ) in terms of θ, if 0° ≤ θ ≤ 360°?

    <p>tan θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what is the relationship between the cosine of the angle of P and P'?

    <p>cos(180° - θ) = -cos θ</p> Signup and view all the answers

    What is the value of sin(180° + θ) in terms of θ?

    <p>sin θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what is the relationship between the tangent of the angle of P and P'?

    <p>tan(180° - θ) = -tan θ</p> Signup and view all the answers

    What is the value of cos(360° + θ) in terms of θ?

    <p>cos θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the line y = x, what is the value of sin(90° + θ) in terms of θ?

    <p>cos θ</p> Signup and view all the answers

    What is the value of tan(180° + θ) in terms of θ?

    <p>tan θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the x-axis, what is the value of cos(90° - θ) in terms of θ?

    <p>sin θ</p> Signup and view all the answers

    What is the value of sin(360° - θ) in terms of θ, if 0° ≤ θ ≤ 360°?

    <p>-sin θ</p> Signup and view all the answers

    What is the value of tan(90° + θ) in terms of θ?

    <p>-cot θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the origin, what is the value of sin(180° + θ) in terms of θ?

    <p>-sin θ</p> Signup and view all the answers

    What is the value of cos(180° - θ) in terms of θ?

    <p>-cos θ</p> Signup and view all the answers

    What is the value of tan(180° - θ) in terms of θ?

    <p>-tan θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what is the value of sin(90° - θ) in terms of θ?

    <p>cos θ</p> Signup and view all the answers

    What is the value of cos(360° + θ) in terms of θ?

    <p>cos θ</p> Signup and view all the answers

    If points P and P' are symmetrical about the line y = x, what are the coordinates of P' if P has coordinates (√3, 1)?

    <p>(1, √3)</p> Signup and view all the answers

    What is the value of sin(180° - θ) in terms of θ?

    <p>sin θ</p> Signup and view all the answers

    What is the value of tan(90° + θ) in terms of θ?

    <p>-tan θ</p> Signup and view all the answers

    What is the phase difference between the sine and cosine graphs?

    <p>90°</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what is the relationship between their sine values?

    <p>sin(θ) = -sin(θ)</p> Signup and view all the answers

    If OP makes an angle θ = 30° with the x-axis, what is the angle of OP' in terms of θ if points P and P' are symmetrical about the y-axis?

    <p>180° - θ</p> Signup and view all the answers

    What is the value of cos(θ) in terms of cos(180° - θ)?

    <p>-cos(180° - θ)</p> Signup and view all the answers

    If points P and P' are symmetrical about the y-axis, what is the relationship between their x-coordinates?

    <p>x = -x</p> Signup and view all the answers

    What is the value of tan(180° - θ) in terms of tan(θ)?

    <p>-tan(θ)</p> Signup and view all the answers

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