Trigonometry
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Last updated 2:38 PM on 6/28/23
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59 Terms
1
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multiply by 180/π
Convert radians to degrees
2
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1
cos (2π) / 0
3
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0
sin (2π) / 0
4
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0
tan (2π) / 0
5
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√3/2
cos (π/6)
6
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1/2
sin (π/6)
7
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√3/3
tan (π/6)
8
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√2/2
cos (π/4)
9
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√2/2
sin (π/4)
10
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1
tan (π/4)
11
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1/2
cos (π/3)
12
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√3/2
sin (π/3)
13
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√3
tan (π/3)
14
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0
cos (π/2)
15
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1
sin (π/2)
16
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undefined
tan (π/2)
17
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√3, √2, √1 all divided by 2
If we go from the bottom angle (π/6) to the top angle (π/3), the values of cos x will be...
18
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√1, √2, √3 all divided by 2
If we go from the bottom angle (π/6) to the top angle (π/3), the values of sin x will be...
19
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values of cos will be negatives, while values of sin will be positive
Rules for values in the II quadrant (notable angles between 2π/3 & 5π/3) are...
20
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values of cos and sin will both be negative
Rules for values in the III quadrant (notable angles between 7π/6 & 4π/3) are...
21
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values of cos will be positive, while values of sin will be negative
Rules for values in the IV quadrant (notable angles between 5π/3 & 11π/6) are...
22
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sin x/cos x, or 1/cot x
tan x=
23
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1/cos x or Hypotenuse/Adjacent
sec x =
24
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1/sin x or Hypotenuse/Opposite
csc x =
25
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cos x/sin x, or 1/tan x
cot x =
26
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f'(u)u'
Chain Rule (Trigonometry) d/dx [f(u)]
27
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The denominator - 1
Rules for angles in the second quadrant
28
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2π/3 (120 degrees)
What's the angle for π/3 in the second quadrant?
29
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3π/4 (135 degrees)
What's the angle for π/4 in the second quadrant?
30
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5π/6 (150 degrees)
What's the angle for π/6 in the second quadrant?
31
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2π/3 -> 120
3π/4 -> 135
5π/6 -> 150
3π/4 -> 135
5π/6 -> 150
Angles in the second quadrant
32
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The denominator + 1
Rule for angles in the third quadrant
33
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7π/6 (210 degrees)
What's the angle for π/6 in the third quadrant?
34
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5π/4 (225 degrees)
What's the angle for π/4 in the third quadrant?
35
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4π/3 (240 degrees)
What's the angle for π/3 in the third quadrant?
36
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The denominator x2 - 1
Rule for angles in the fourth quadrant
37
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5π/3 (300 degrees)
What's the angle for π/3 in the fourth quadrant?
38
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7π/4 (315 degrees)
What's the angle for π/4 in the fourth quadrant?
39
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11π/6 (330 degrees)
What's the angle for π/6 in the fourth quadrant?
40
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always be negative
Derivatives of functions with "co" in their name will...
41
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just be each other
Derivatives of cos and sin will....
42
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always be squared, and either secant or cosecant
Derivatives of tangent and cotangent will...
43
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just be themselves multiplied by either tan or cotangent
Derivatives of secant and cosecant will...
44
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-sin x
d/dx [cos x]
45
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cos x
d/dx [sin x]
46
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sec^2 x
d/dx [tan x]
47
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-csc^2 x
d/dx [cot x]
48
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-csc x cot x
d/dx [csc x]
49
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sec x tan x
d/dx [sec x]
50
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To find the angle which gives us an specific value
Inverse Trig Functions asks us...
51
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arctan u, arcos u, & arc sin u
The Inverse Trig Functions are
52
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u' / 1+u^2
d/dx [arctan u]
53
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-u'/√(1-u^2)
d/dx [arccos u]
54
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u'/√(1-u^2)
d/dx [arcsin u]
55
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1
sin^2 x + cos^2 x =
56
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tan^2 x + 1
sec^2 x =
57
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cot^2 x + 1
csc^2 x =
58
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1st and 2d quadrants, 0/2π - π
Range of arc cos x
59
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4th and 1st quadrant, 3π/2 - π/2
Range of arcsin x and arctan x
Note 
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