DAT QR 2 - Trigonometry

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Author:
NavyArmy
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293663
Filename:
DAT QR 2 - Trigonometry
Updated:
2015-01-25 23:40:47
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DAT QR Quantitative Reasoning Trig Trigonometry
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DAT,QR
Description:
Gold Standard DAT QR Review - Chapter 6 (Trigonometry) Flashcards
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  1. What is Sine?
    • Sine =   Opposite_
    •           Hypotenuse

    i.e. sin(θ) = a/h

  2. What is Cosine?
    • Cosine =  Adjacent  
    •              Hypotenuse

    i.e. cos(θ) = b/h

  3. What is Tangent?




  4. a) What is secant?

    b) What is cosecant?

    c) What is cotangent?
    a)

    b)

    c)
  5. Unit circle (with degree/radian angles and corresponding point values)
  6. How many degrees is radians?
    360°

    Thus, 1 radian =
  7. What are the radians, sine, and cosine equivalent for 0°?
    • Radians: 0
    • Sine: 0
    • Cosine: 1
  8. What are the radians, sine, and cosine equivalent for 30°?
    • Radians:
    • Sine:
    • Cosine:
  9. What are the radians, sine, and cosine equivalent for 45°?
    • Radians:
    • Sine:  or
    • Cosine: or

    Note: the values remain unchanged except for the signs as the angle passes through the different quadrants (moving counterclockwise from 0°: Q's I, II, III, IV).
  10. What are the radians, sine, and cosine equivalent for 60°?
    • Radians:
    • Sine:
    • Cosine:
  11. What are the radians, sine, and cosine
    equivalent for 90°?
    • Radians:
    • Sine: 1
    • Cosine: 0
  12. Indicate the signs of sine, cosine, and tangent in quadrant I of the unit circle.
    • I: sin +
    •    cos +
    •    tan +
  13. Indicate the signs of sine, cosine, and tangent
    in quadrant II of the unit circle.
    • II: sin +
    •     cos -
    •     tan -
  14. Indicate the signs of sine, cosine, and tangent
    in quadrant III of the unit circle.
    • III:  sin -  
    •       cos -
    •       tan +
  15. Indicate the signs of sine, cosine, and tangent in quadrant IV of the unit circle.
    • IV: sin -
    •      cos +
    •      tan -
  16. At what point does the sine function reach a maximum (i.e. +1)?


    • = 360°
    • n = any integer (number of cycles)

  17. At what point is the x-intercept located for the sine function?


    • n = any integer (number of cycles)
  18. At what point does the sine function reach a minimum (i.e. -1)?



    • n = any integer (number of cycles)
  19. At what point does the cosine function reach a maximum (i.e. +1)?
    It reaches a maximum at

    • n = any integer (number of cycles)
  20. At what point is the x-intercept located for the cosine function?


  21. At what point does the cosine function reach a minimum (i.e. -1)?


    n is any integer
  22. What are the corresponding periodicity (function repeats itself) of the following trig functions:

    a) tangent & cotangent
    b) sine & cosine
    • a) -periodic
    •     - it also has vertical asymptotes (lines where the function never crosses)
    •     - vert. asymptote at for every odd integer n (where cos is 0 --> sin / 0 is undefined)

    b) -periodic
  23. What is the inverse of a trig function?
    It is taking the value of an angle and finding out what the angle is.

    • e.g. sin (sin-1(x)) = x
    • Thus, sin(θ) = x and sin-1(x) = θ
  24. Recall 8 trig identities.
    a) sin2θ + cos2θ = 1

    - derived from the Pythagorean Theorem (sin and cos are legs of a triangle while the hyp = radius (1))

    b) tan2θ + 1 = sec2θ

    c) 1 + cot2θ = csc2θ

    d) sin(2θ) = 2(sinθ)(cosθ)

    e) cos(2θ) = 1 - 2(sin2θ)

    f) tan(2θ) =

    g) sin(-θ) = -sin(θ)  <-- odd function

    h) cos(θ) = cos(-θ)  <-- even function

    Note: recall "odd" and "even" functions:

    even: f(x) = f(-x) --> graph symm. along y-axis

    odd: f(x) ≠ f(-x) --> graph symm. along its origin

           instead: f(x) = -f(-x) or f(-x) = -f(x)
  25. Recall trig identities for sin(θ) & cos(θ) when adding 2 to a point on the unit circle
    cos(θ) = cos(θ + 2)

    sin(θ) = sin(θ + 2)

    Note: 2 is just one full cycle.
  26. Recall trig function (sum or diff. of two angles) for sine:

    sin (x + y) = ?
    sin (x - y) = ?
    • sin (x + y) = sin(x)cos(y) + cos(x)sin(y)
    • sin (x - y) = sin(x)cos(y) - cos(x)sin(y)

    Mnemonic: sine is "sum"thing that switches :)

    ** start with a "+" (or "-") --> stays with a "+" (or "-") on the other equation.
  27. What is the tangent addition formula --> tan(α + β)?
  28. Recall trig function (sum/diff of two angles) for cosine:

    cos (x + y) = ?
    cos (x - y) = ?
    • cos (x + y) = cos(x)cos(y) - sin(x)sin(y)
    • cos (x - y) = cos(x)cos(y) + sin(x)sin(y)

    Mnemonic: "opposite" the functions did not "switch."
  29. What are polar coordinates?
    A system that uses the hypotenuse of the triangle (r) and the angle from the x-axis (θ).

    - instead of two distance components (as in a Cartesian plane x & y), this system use one radial distance component (distance from origin) and an angle component.

    - A point is written as the ordered pair (r, θ).
  30. Identities to use to convert points between polar and Cartesian coordinates.
    i. r2 = x2 + y2

    ii. x = (r) x (cos(θ))

    iii. y = (r) x (sin(θ))
  31. What are the trig properties for Sum or Differences of Two Angles?
  32. What are the trig properties for Cofunction Identities (for radians & degrees)?
  33. What are the trig properties for Odd-Even Identities?

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