Year 2 chapter 7: Trigonometry And Modelling

Question 1

What is sin(A+B) equivalent to?

Answer 1

SinACosB + CosASinB

Question 2

What is cos(A+B) equivalent to?

Answer 2

CosACosB - SinASinB

Question 3

What is tan(A+B) equivalent to?

Answer 3

(TanA + TanB) ➗ (1 - TanATanB)

Question 4

What is sin(A-B) equivalent to?

Answer 4

SinACosB - CosASinB

Question 5

What is cos(A-B) equivalent to?

Answer 5

CosACosB + SinASinB

Question 6

What is tan(A-B) equivalent to?

Answer 6

(TanA - TanB) ➗ (1 + TanATanB)

Question 7

What is sin(2A) equivalent to?

Answer 7

2sin(A)cos(A)

Question 8

What is cos(2A) equivalent to?

Answer 8

Cos²A - sin²A = 2cos²A - 1 = 1 - 2sin²A

Question 9

What is tan(2A) equivalent to?

Answer 9

2tan(A) ➗ (1 - tan²(A))

Question 10

If ‘Rcos(x-‘alpha’) = acos(x) + bsin(x)’, and you know the values of ‘a’ and ‘b’ (‘a’ and ‘b’ are positive values), how to you find ‘R’ and ‘x’?

Answer 10

. Rcos(x-‘alpha’) = Rcos(x)cos(‘alpha’) + Rsin(x)sin(‘alpha’) = acos(x) + bsin(x).
. So ‘Rcos(‘alpha’) = a’ and ‘Rsin(‘alpha’) = b’.
. Then use simultaneous equations to find out ‘R’ and ‘x’, by using the rules of ‘sin²x + cos²x = 1’ or ‘sinx/cosx = tanx’.