Trigonometry And Modelling

Question 1

State the equation for sin(A + B) and the equation for sin(A - B)

Answer 1

sin(A + B) = sinAcosB + cosAsinB

sin(A - B) = sinAcosB - cosAsinB

Question 2

State the equation for cos(A + B) and the equation for cos(A - B)

Answer 2

cos(A + B) = cosAcosB - sinAsinB

cos (A - B) = cosAcosB + sinAsinB

Question 3

State the equation for tan(A + B) and the equation for tan(A - B)

Answer 3

tan(A + B) = tanA + tan(-B)/1 - tanAtan(-B)

tan(A - B) = tanA - tanB/1 + tanAtanB

Question 4

Derive the equation for sin2A

Answer 4

sin2A = sin(A + A)
= sinAcosA + sinAcosA
= 2sinAcosA

Question 5

Derive the equation for cos2A

Answer 5

cos2A = cos(A + A)
= cosAcosA - sinAsinA
= cos²A - sin²A
= cos²A - (1 - cos²A)
= 2cos²A - 1

Or cos2A = 1 - 2sin²A

Question 6

Derive the equation for tan2A

Answer 6

tan2A = tan(A + A)
= tanA + tanA/1 - tanAtanA
= 2tanA/1 - tan²A