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Trig and Precal

  • A2-11: CIRCUMFERENCE VS. DIAMETER - CHAIN ON CYLINDER

    A2-11
    Show the relationship between the diameter and the circumference of a circle
    A chain, originally wound around a cylinder, is unwound. The diameter of the cylinder can be compared with the length of the chain wound off one turn, so the value of pi may be approximated. This is valuable to introduce students to the concept of radians, a unit common in physics formulae but rarely encountered in daily use.

    This can also be used to introduce concepts related to estimation and dimensionality. Encourage students to make predictions about the relationships of the lengths, then try them out hands-on so they can test and analyze their predictions.
    A2, D4

  • A2-13: ELLIPSE DRAWING BOARD

    A2-13
    Demonstrate one method of drawing ellipses
    The ends of a string loop are hooked around two pegs on the board and kept tight by the chalk holder. Moving the string around one complete turn produces an ellipse. This procedure creates the locus of points where R1 + R2 = Constant, the equation for an ellipse. Changing the peg position changes the eccentricity of the ellipse.

    Consider inviting students to make predictions about how the shape of the ellipse will change in response to changing the foci in different ways. This can be related to a variety of mathematical and astronomical phenomena.

    FS2

  • A2-14: DISSECTIBLE CONE

    A2-14
    Illustration of the conic sections
    Wooden cone with four separable parts -- one for each conic section. Invite students up to examine the cone and its dissection. Alternatively, show the intact cone and invite students to make predictions about the shapes formed by slicing along the different lines.
    A2

  • A2-32: HEIGHT MEASUREMENT BY TRIGONOMETRY

    A2-32
    Determine the height of a student using trigonometry
    Determine the height h of a student by measuring the distance x of the student from the protractor and the angle a of the top of the student from the floor: h = x tan a. Compare the experimental value with a direct measurement using the two-meter stick.
    A2

    g

  • A2-33: DIRECTION COSINES MODEL

    A2-33
    Aid in perception of the components of a three-dimensional vector

    An arbitrary vector in three-dimensional space is shown along with projections along the three orthogonal axes. Observe how the angles alpha, beta, gamma are defined.

    Emphasize that the angle between the vector and any axis is not the same as the angle between the axis and the projection of the vector onto a plane defined by two axes.

    Consider passing it around for students to get a hands-on feel for the functions, but be careful of the vector tips.
    A2