DAT QR 2 - Trigonometry

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  1. What is Sine?
    • Sine =   Opposite_
    •           Hypotenuse

    i.e. sin(θ) = a/h

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

    i.e. cos(θ) = b/h

    Image Upload
  3. What is Tangent?
    Image Upload

    Image Upload

    Image Upload
  4. a) What is secant?

    b) What is cosecant?

    c) What is cotangent?
    a) Image Upload

    b) Image Upload

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

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

    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: Image Upload
    • Sine: Image Upload
    • Cosine: Image Upload
  11. What are the radians, sine, and cosine
    equivalent for 90°?
    • Radians: Image Upload
    • 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)?
    Image Upload

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

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

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


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

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

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

    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) Image Upload-periodic
    •     - it also has vertical asymptotes (lines where the function never crosses)
    •     - vert. asymptote at Image Upload for every odd integer n (where cos is 0 --> sin / 0 is undefined)

    b) Image Upload-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) = Image Upload

    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 2Image Upload to a point on the unit circle
    cos(θ) = cos(θ + 2Image Upload)

    sin(θ) = sin(θ + 2Image Upload)

    Note: 2Image Upload 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)?
    Image Upload
  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?
    Image Upload
  32. What are the trig properties for Cofunction Identities (for radians & degrees)?
    • Image Upload
    • Image Upload
  33. What are the trig properties for Odd-Even Identities?
    Image Upload

Card Set Information

Author:
NavyArmy
ID:
293663
Filename:
DAT QR 2 - Trigonometry
Updated:
2015-01-26 04:40:47
Tags:
DAT QR Quantitative Reasoning Trig Trigonometry
Folders:
DAT,QR
Description:
Gold Standard DAT QR Review - Chapter 6 (Trigonometry) Flashcards
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