P2.7 Trig. & Modelling

Question 1

sin(A +/- B) =

Answer 1

sinAcosB +/- cosAsinB

Question 2

cos(A +/- B) =

Answer 2

cosAcosB -/+ sinAsinB

Question 3

tan(A +/- B)

Answer 3

tanA +/- tanB / 1 -/+ tanAtanB

Question 4

sin2A =

Answer 4

2sinAcosA

Question 5

cos2A =

Answer 5

cos^2A - sin^2A
2cos^2A -1
1-2sin^2A

Question 6

tan2A =

Answer 6

2tanA / 1-tan^2A

Question 7

when solving trig. equations with sin & cos…

Answer 7

put sinx on one side & cosx on the other
then divide by cos & constant in front of sinx to get tanx =
or Rsin(x+a)

Question 8

when finding the time for one complete revolution for something defined with a trig. equation…

Answer 8

find consecutive times it is at max. height

Question 9

describe how to simplify acosx +/- bsinx

Answer 9

can be expressed in the form Rsin(x +/- α)
or Rcos(x -/+ α)
R > 0, 0 < α < 90
R = √(a^2 + b^2)

see Baldwin notes or e.g.s on p182 P2 textbook

Question 10

proving trig. identities

Answer 10

practice

Question 11

modelling with Rsin(x + α) and Rcos(x + α)

Answer 11

v common exam Q
see Wilson OneNote & pg189 P2 textbook