Trigonometry Flashcards

1
Q

Side lengths for 45 degree triangle

A

Hypotenuse = x√2
45 leg = x

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2
Q

Side lengths for 60-30 degree triangle

A

Hypotenuse = 2x
60 leg = x√3
30 leg = x

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3
Q

sin θ

A

opp / hyp

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4
Q

cos θ

A

adj / hyp

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5
Q

tan θ

A

opp / adj

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6
Q

csc θ

A

reciprocal of sine
hyp / opp

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7
Q

sec θ

A

reciprocal of cosine
hyp / adj

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8
Q

cot θ

A

reciprocal of tangent
adj / opp

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9
Q

sin 30

A

cos 60

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10
Q

cos 30

A

sin 60

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11
Q

tan 30

A

1 / tan 60 (reciprocals)

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12
Q

sin 45

A

cos 45

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13
Q

tan 45

A

1

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14
Q

Unit Circle, 30 degree Q1 coordinate

A

(√3 / 2, 1/2)

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15
Q

Unit Circle, 45 degree Q1 coordinate

A

(√2/2, √2/2)

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16
Q

Unit Circle, 60 degree Q1 coordinate

A

(1/2, √3 / 2)

17
Q

Turning degrees to radians

A

degree divided by 180, include pi
degrees(pi/180)

18
Q

Turning radians to degrees

A

multiply radians by 180, then divide number by denominator.
radians(180/pi)

19
Q

Co-terminal angles

A

Angles in standard position with the same terminal side are co-terminal angles. (full 360 around both directions)
- if adding 360 does not result in positive answer, keep adding 360 and vise versa
2pi = 360

20
Q

Reference angles

A

the positive angle formed on the x-axis.
- has to touch x-axis
- need to be in quadrant 1

21
Q

Trig functions, sin θ

A

y coordinate

22
Q

Trig functions, cos θ

A

x coordinate

23
Q

Trig functions, tan θ

A

y / x
sin / cos

24
Q

Q1 positive trig functions

25
Q2 positive trig functions
sin θ, csc θ
26
Q3 positive trig functions
tan θ, cot θ
27
Q4 positive trig functions
cos θ, sec θ
28
How to look at inverse trig functions
sin -1 (1/2) ask, 'where is y equal to. . .?' to the 1/2 look at the sign as well
29
Quotient identities
tan θ = sin θ/cosθ cot θ = cos θ/sin θ
30
Reciprocal identities
sin θ = 1/csc θ cos θ = 1/sec θ tan θ = 1/cot θ the same with csc, sec, cot flipped postions
31
Pythagorean identities
cos^2 θ + sin^2 θ = 1 tan^2 θ +1 = sec^2 θ cot^2 θ +1 = csc^2 θ
32
Helpful techniques for simplifying expressions
Change everything to sine or cosine factoring to simplify expression if possible get common denominators if there are fractions multiply by conjugates