10 - trig - graphs + equations Flashcards
1
Q
sin graph
A
wave
starts at origin
- repeats every 360
- range -1< sin(x) <1
2
Q
cos graph
A
bucket
starts at (0,1)
- repeats every 360
-range -1< sin(x) <1
3
Q
tan graph
A
- repeats every 180
- roots …-180, 0, 180…
- range tan(x) E R (no min/max)
- asymptotes x = …+-90, +-270…
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)
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()
6
Q
trig identities
A
sin()^2 + cos()^2 = 1
tan () = sin()/cos()
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)
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