# Trigonometry

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multiply by 180/π

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## Tags and Description

### 59 Terms

1

multiply by 180/π

Convert radians to degrees

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2

1

cos (2π) / 0

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3

0

sin (2π) / 0

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4

0

tan (2π) / 0

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5

√3/2

cos (π/6)

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6

1/2

sin (π/6)

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7

√3/3

tan (π/6)

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8

√2/2

cos (π/4)

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9

√2/2

sin (π/4)

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10

1

tan (π/4)

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11

1/2

cos (π/3)

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12

√3/2

sin (π/3)

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13

√3

tan (π/3)

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14

0

cos (π/2)

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15

1

sin (π/2)

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16

undefined

tan (π/2)

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17

√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...

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18

√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...

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19

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...

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20

values of cos and sin will both be negative

Rules for values in the III quadrant (notable angles between 7π/6 & 4π/3) are...

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21

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...

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22

sin x/cos x, or 1/cot x

tan x=

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23

1/cos x or Hypotenuse/Adjacent

sec x =

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24

1/sin x or Hypotenuse/Opposite

csc x =

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25

cos x/sin x, or 1/tan x

cot x =

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26

f'(u)u'

Chain Rule (Trigonometry) d/dx [f(u)]

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27

The denominator - 1

Rules for angles in the second quadrant

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28

2π/3 (120 degrees)

What's the angle for π/3 in the second quadrant?

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29

3π/4 (135 degrees)

What's the angle for π/4 in the second quadrant?

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30

5π/6 (150 degrees)

What's the angle for π/6 in the second quadrant?

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31

2π/3 -> 120 3π/4 -> 135 5π/6 -> 150

Angles in the second quadrant

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32

The denominator + 1

Rule for angles in the third quadrant

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33

7π/6 (210 degrees)

What's the angle for π/6 in the third quadrant?

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34

5π/4 (225 degrees)

What's the angle for π/4 in the third quadrant?

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35

4π/3 (240 degrees)

What's the angle for π/3 in the third quadrant?

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36

The denominator x2 - 1

Rule for angles in the fourth quadrant

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37

5π/3 (300 degrees)

What's the angle for π/3 in the fourth quadrant?

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38

7π/4 (315 degrees)

What's the angle for π/4 in the fourth quadrant?

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39

11π/6 (330 degrees)

What's the angle for π/6 in the fourth quadrant?

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40

always be negative

Derivatives of functions with "co" in their name will...

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41

just be each other

Derivatives of cos and sin will....

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42

always be squared, and either secant or cosecant

Derivatives of tangent and cotangent will...

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43

just be themselves multiplied by either tan or cotangent

Derivatives of secant and cosecant will...

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44

-sin x

d/dx [cos x]

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45

cos x

d/dx [sin x]

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46

sec^2 x

d/dx [tan x]

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47

-csc^2 x

d/dx [cot x]

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48

-csc x cot x

d/dx [csc x]

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49

sec x tan x

d/dx [sec x]

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50

To find the angle which gives us an specific value

Inverse Trig Functions asks us...

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51

arctan u, arcos u, & arc sin u

The Inverse Trig Functions are

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52

u' / 1+u^2

d/dx [arctan u]

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53

-u'/√(1-u^2)

d/dx [arccos u]

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54

u'/√(1-u^2)

d/dx [arcsin u]

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55

1

sin^2 x + cos^2 x =

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56

tan^2 x + 1

sec^2 x =

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57

cot^2 x + 1

csc^2 x =

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58

1st and 2d quadrants, 0/2π - π

Range of arc cos x

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59

4th and 1st quadrant, 3π/2 - π/2

Range of arcsin x and arctan x

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