# DAT QR 2 - Trigonometry

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

i.e. sin(θ) = a/h

2. What is Cosine?
•              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°

7. What are the radians, sine, and cosine equivalent for 0°?
• Sine: 0
• Cosine: 1
8. What are the radians, sine, and cosine equivalent for 30°?
• Sine:
• Cosine:
9. What are the radians, sine, and cosine equivalent for 45°?
• 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°?
• Sine:
• Cosine:
11. What are the radians, sine, and cosine
equivalent for 90°?
• 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?
 Author: NavyArmy ID: 293663 Card Set: 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 Show Answers: