P2.5 Radians

Question 1

define 1 radian

Answer 1

the angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle

Question 2

360 =
180 =
1 radian =

Answer 2

2π
π
180/π

Question 3

30, 45, 60, 90 in radians

Answer 3

π/6
π/4
π/3
π/2

Question 4

exact values of trig. ratios of these angles measured in radians

Answer 4

see pg 117 P1 textbook

Question 5

describe CAST diagram in radians

Answer 5

see pg 117 P1 textbook

Question 6

what is the formula for arc length using radians?

Answer 6

l = rθ

Question 7

what is the formula for the area of a sector using radians?

Answer 7

A = 1/2 r^2 θ
smaller area is minor sector
larger area is major sector

Question 8

what is the formula for the area of a segment & how is it derived?

Answer 8

A = 1/2 r^2 (θ - sinθ)

derived by subtracting the area of the triangle from the area of the sector
1/2absinC –> 1/2r^2 sinC
A = 1/2r^2θ - 1/2r^2sinθ

Question 9

solving trig. equations in radians

Answer 9

practice

Question 10

describe the small angle approximations

Answer 10

when θ is small & measured in radians:
sinθ = θ
cosθ = 1 - θ^2/2
tanθ = θ

Question 11

comment on the validity of the answers using small angle approximations

Answer 11

_ is a small angle & therefore valid
_ is not a small angle & therefore invalid
–> too big for small angle approximations