trigonometric identities year 2

Question 1

degrees to radians

Answer 1

/360 then multiply by 2pie

Question 2

arc length in radians

Answer 2

θ × r

Question 3

arc length in degrees

Answer 3

. θ/ 360 × 2πr

Question 4

sector area degrees

Answer 4

(θ/360º) × πr2

Question 5

sector area radians

Answer 5

1/2 × r2θ

Question 6

area of segment radians

Answer 6

(½) × r2 (θ – Sin θ)

Question 7

small angle formulas

Answer 7

given in formula booklet but always look out for them when says angles are small

Question 8

percentage error

Answer 8

absolute error/correct value x 100

Question 9

sec(x)

Answer 9

1/cos(x)

Question 10

cosec(x)

Answer 10

1/sin(x)

Question 11

cot(x)

Answer 11

1/tan(x)
OR
cosx/sinx

Question 12

secx2=

Answer 12

1+tanx2

Question 13

cosecx2=

Answer 13

1+ cotx2

Question 14

tanx

Answer 14

sinx/cosx

Question 15

sinx2+cosx2

Answer 15

1

Question 16

double angle formula

Answer 16

given on formula sheet, but always look out for when you see a 2x or any equation/ function in the correct form

Question 17

sin2A

Answer 17

2sinAcosA
use double angle formula to find, but plug in both A and B as A

Question 18

cos2A

Answer 18

cos2A-sin2A
OR
2cos2A-1
OR
1-2sin2A

Question 19

REARANGING cos2A fomula to give different identities

Answer 19

0.5(1+cos2A)= cos2A

sin2A= 0.5(1-cos2A)

Question 20

inverse functions

Answer 20

Inverse functions can be written as arcsinx or arccosx for example.
The graphs of the inverse functions are reflections of the original trigonometric graphs in the line y=x
These graphs have many to one functions so must be restricted to ensure one to one function

Question 21

range and domain of inverse graphs

Answer 21

FUNCTION: DOMAIN: RANGE:
y=sinx -π/2<y<π/2 -1<.-y<.-1
y=arcsinx -1<.x<.1 -π/2<.y<.π/2
y=cosx 0<.x<.π -1<.y<.1
y=arccosx -1<.x<.1 0<.y<.π
y=tanx -π/2<y<π/2 y is real
y=arctanx x is real -π/2<y<π/2