10 - trig - graphs + equations

Question 1

sin graph

Answer 1

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

Question 2

cos graph

Answer 2

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

Question 3

tan graph

Answer 3

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

Question 4

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

Answer 4

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

Question 5

sin and cos triangle

Answer 5

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()

Question 6

trig identities

Answer 6

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

Question 7

sin/ cos/ tan angle rules

Answer 7

• 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)

Question 8

unit circle

Answer 8

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