2 - 7 radian measure

Question 1

360º

Answer 1

2pi rad

Question 2

how to do sin(pi - θ)

Answer 2

draw the sin graph
mark on θ
mark on pi-θ
compare them
will be either sinθ or -sinθ

Question 3

arcsin/ tan/ cos graph

Question 4

sin(arcsin(x)) vs arcsin(sin(x))

Answer 4

sin(arcsin(x)) = x
but arcsin(sin(x)) doesnt always = x - only in the range pi/2 > -pi/2

Question 5

modelling with trig functions

Answer 5

y = a sin(bx) and a cos(bx)
has amplitude a and period 2pi/b

Question 6

y = a sin b(x+c) +d

Answer 6

amplitude = a
central value = d
minimum =d-a max = d+a
period = 2pi/b

Question 7

length of an arc

Answer 7

l = rθ
where θ is in radians
because l/2pi*r = θ/2pi
major arc = longer one minor = shorter
minor arc subtends an angle θ at the centre of the circle

Question 8

area of a sector

Answer 8

A = 1/2r^2 θ

Question 9

chord

Answer 9

joins 2 points on the edge of a circle

Question 10

segment

Answer 10

area from chord to circumference

Question 11

length of a chord

Answer 11

AB = r√2(1-cosθ)

Question 12

area of a segment

Answer 12

1/2r^2(θ-sinθ)

Question 13

small angle approximations

Answer 13

sinθ = θ
cosθ = 1-1/2θ^2
tanθ = θ