Gr 10 Math Ch 4: Defining Ratios in the Cartesian Plane
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Questions and Answers

What does the tangent ratio represent for a point in the Cartesian plane?

  • The angle between the line and the negative x-axis
  • The length of the line from the origin to the point
  • The ratio of the opposite side to the adjacent side of a right triangle (correct)
  • The ratio of the angle to the x-axis

    • If the coordinates of point P are (2, 3), what is the value of the tangent ratio used to find angle A?

  • $3 + 2$
  • $ rac{3}{2}$ (correct)
  • $ rac{2}{3}$
  • $ rac{1}{ rac{2}{3}}$

    • How is angle B related to angle α for the point Q(-2, 3)?

  • B and α are the same angle
  • B + α = 90^ ext{o}
  • B + α = 180^ ext{o} (correct)
  • B and α are complementary angles

    • What is the value of angle B when the coordinates for point Q(-2, 3) are used?

    <p>123.7^ ext{o}</p> Signup and view all the answers

    What is the radius of the circle centered at the origin if it passes through point P(2, 3)?

    <p>$ ext{sqrt}(2^2 + 3^2)$</p> Signup and view all the answers

    Which statement about the angle θ formed by point P(x, y) and the x-axis is true?

    <p>θ is the angle between the line OP and the x-axis</p> Signup and view all the answers

    When working with the angle of a point in the fourth quadrant, how is the tangent ratio affected?

    <p>The tangent is always negative</p> Signup and view all the answers

    What relationship holds true between the angles formed with the positive and negative x-axes?

    <p>They are supplementary angles</p> Signup and view all the answers

    In which quadrant are only the sine and cosecant trigonometric ratios positive?

    <p>Quadrant II</p> Signup and view all the answers

    What is the value of $ an 45^ heta$?

    <p>1</p> Signup and view all the answers

    Which trigonometric ratio is undefined at $90^ heta$?

    <p>$ an 90^ heta$</p> Signup and view all the answers

    What is the sine of $30^ heta$?

    <p>$ rac{1}{2}$</p> Signup and view all the answers

    What is the relationship between sine and cosecant?

    <p>$ ext{cosec } heta = rac{1}{ ext{sin } heta}$</p> Signup and view all the answers

    Which of the following statements is true regarding the trigonometric functions in Quadrant IV?

    <p>Only cosine and secant are positive.</p> Signup and view all the answers

    Which trigonometric ratio is positive in Quadrant II?

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

    What is the value of tan $60^ heta$?

    <p>$ ext{sqrt}(3)$</p> Signup and view all the answers

    Which of the following statements is true about cosecant?

    <p>It is the reciprocal of sine.</p> Signup and view all the answers

    For the angle $0^ heta$, what is the value of sin θ?

    <p>0</p> Signup and view all the answers

    In which quadrant are tan θ and cot θ positively defined?

    <p>Quadrant III</p> Signup and view all the answers

    What is the cosine of angle $90^ heta$?

    <p>0</p> Signup and view all the answers

    What is the value of the tangent ratio for angle A formed by the point P(2, 3)?

    <p>$1.5$</p> Signup and view all the answers

    Which of the following angles represents angle B for point Q(-2, 3)?

    <p>$123.7^ heta$</p> Signup and view all the answers

    If point P is located at (x, y) in the Cartesian plane, which formula represents the length from the origin to point P?

    <p>$ ext{length} = ext{sqrt}(x^2 + y^2)$</p> Signup and view all the answers

    What relationship holds between angles A and B when considering point Q(-2, 3) and point P(2, 3)?

    <p>Angle B is the reflection of angle A across the x-axis.</p> Signup and view all the answers

    For a point located in the second quadrant, which statement about the tangent ratio is true?

    <p>The tangent is negative.</p> Signup and view all the answers

    Angle α for point Q(-2, 3) is formed with which axis?

    <p>The negative x-axis</p> Signup and view all the answers

    What is the measure of angle α given that $ an heta = rac{3}{2}$?

    <p>$56.3^ heta$</p> Signup and view all the answers

    When plotting points in the Cartesian plane, which quadrant is characterized by positive x and negative y coordinates?

    <p>Quadrant IV</p> Signup and view all the answers

    Which trigonometric ratio is positive in Quadrant III?

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

    What is the sine value of $45^ heta$?

    <p>$\frac{1}{\sqrt{2}}$</p> Signup and view all the answers

    When the angle θ is $90^ heta$, what is the value of cos θ?

    <p>0</p> Signup and view all the answers

    In which quadrant are only the cosine and secant trigonometric ratios positive?

    <p>Quadrant IV</p> Signup and view all the answers

    Which of the following statements is true regarding the tangent of $30^ heta$?

    <p>It equals $\frac{1}{\sqrt{3}}$.</p> Signup and view all the answers

    Which trigonometric ratio is defined as $\frac{y}{x}$?

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

    If point Q is located at (-2, 3) in the Cartesian plane, what is the general formula to determine angle B formed between line OQ and the positive x-axis?

    <p>$B = 180^ heta - an^{-1}(3/2)$</p> Signup and view all the answers

    What is the correct relationship between angle α and angle B when considering point Q(-2, 3) in the Cartesian plane?

    <p>$B + heta = 180^ heta$</p> Signup and view all the answers

    When determining the angle θ formed by point P(2, 3) with the x-axis, which of the following represents the radius of the circle centered at the origin?

    <p>$r = ext{sqrt}(2^2 + 3^2)$</p> Signup and view all the answers

    Which of the following statements correctly describes the coordinates of point P(2, 3) in relation to angle A?

    <p>The coordinates indicate that angle A is in the first quadrant.</p> Signup and view all the answers

    For angle B formed by point Q(-2, 3), which of the following correctly describes the tangent ratio in this case?

    <p>$ an B = rac{3}{-2}$</p> Signup and view all the answers

    What would be the approximate degree measure of angle A formed at point P(2, 3)?

    <p>$36.9^ heta$</p> Signup and view all the answers

    When plotting a point P(x, y) in relation to the radius r, which of the following statements is true?

    <p>The radius is determined by $r = ext{sqrt}(x^2 + y^2)$.</p> Signup and view all the answers

    In dealing with angles in the Cartesian plane, which statement correctly compares angles formed in the first and second quadrants?

    <p>Angle B is always the supplement of angle A.</p> Signup and view all the answers

    In which quadrant is the sine value positive and the tangent value undefined?

    <p>Quadrant II</p> Signup and view all the answers

    Given the angle $45^\circ$, what is the value of cosecant?

    <p>$\sqrt{2}$</p> Signup and view all the answers

    Which trigonometric ratio is represented by the formula $\frac{r}{y}$?

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

    What is the tangent value for angle $30^\circ$?

    <p>$\frac{1}{\sqrt{3}}$</p> Signup and view all the answers

    For angles in Quadrant IV, which of the following trigonometric ratios is positive?

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

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