Trigonometric proofs

Question 1

1 - sin^2

Answer 1

cos^2

Question 2

1 - cos^2

Answer 2

sin^2

Question 3

sin^2 + cos^2

Answer 3

= 1

Question 4

how to turn cos(A) into sin(A)

Answer 4

Make all cos(A) into cos(90-A)
Cos(90-A) = sin(90)

Question 5

Cos(90 - (A + B))

Answer 5

= Sin(A + B)

Question 6

Sin(90-A)

Answer 6

Cos(A)

Question 7

Cos(-B)

Answer 7

= Cos(B)

Question 8

Sin(-B)

Answer 8

= -sin(B)

Question 9

Sin(A+B) proof

Answer 9

1. Use Cos(A-B)
2. Replace all A with 90 - A
3. Cos(90-(A+B)) = Sin(A+B)
   Remember to state changes e.g. …since cos(90-{/}) = sin({/})

Question 10

Cos(2A) = square - square
Proof

Answer 10

1. Using cos(A+B)
2. Change B to A

Question 11

Cos2A = 1 - 2square
Proof

Answer 11

1. Use Cos2A = square - square
2. cos^2 = (1-sin^2)

Question 12

Cos2A = 2square - 1 proof

Answer 12

1. Use Cos2A = square - square
2. sin^2 = (1-cos^2)

Question 13

Period of function

Answer 13

2pi / b
b is co-ef of x
Eg. Sin(3x)
Period is 2pi / 3