10 - trig - graphs + equations Flashcards

1
Q

sin graph

A

wave
starts at origin
- repeats every 360
- range -1< sin(x) <1

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2
Q

cos graph

A

bucket
starts at (0,1)
- repeats every 360
-range -1< sin(x) <1

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3
Q

tan graph

A
  • repeats every 180
  • roots …-180, 0, 180…
  • range tan(x) E R (no min/max)
  • asymptotes x = …+-90, +-270…
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4
Q

how to find sin/cos/tan of 30,60,45

A

use right angled isosceles triangle that is 1x1 (for 45)
uses equilateral triangle of 2x2x2 cut in half (for 30 and 60)

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5
Q

sin and cos triangle

A

hypotenuse 1 and sides sin() and cos()
uses pythagorus to show - sin()^2 + cos()^2 = 1
find gradient of the hypotenuse to show - tan () = sin()/cos()

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6
Q

trig identities

A

sin()^2 + cos()^2 = 1
tan () = sin()/cos()

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7
Q

sin/ cos/ tan angle rules

A
  • sin(x) = sin(180 - x)
  • cos(x) = cos(360 - x)
  • sin and cos repeat every 360 and tan every 180
  • sin (x) = cos(90 - x)
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8
Q

unit circle

A
  • has radius of 1
  • point p on a unit circle has coordinates (cos(), sin())
  • OP has gradient tan()
  • angles are measured anticlockwise
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