Trigonometric proofs Flashcards
1
Q
1 - sin^2
A
cos^2
2
Q
1 - cos^2
A
sin^2
3
Q
sin^2 + cos^2
A
= 1
4
Q
how to turn cos(A) into sin(A)
A
Make all cos(A) into cos(90-A)
Cos(90-A) = sin(90)
5
Q
Cos(90 - (A + B))
A
= Sin(A + B)
6
Q
Sin(90-A)
A
Cos(A)
7
Q
Cos(-B)
A
= Cos(B)
8
Q
Sin(-B)
A
= -sin(B)
9
Q
Sin(A+B) proof
A
- Use Cos(A-B)
- Replace all A with 90 - A
- Cos(90-(A+B)) = Sin(A+B)
Remember to state changes e.g. …since cos(90-{/}) = sin({/})
10
Q
Cos(2A) = square - square
Proof
A
- Using cos(A+B)
- Change B to A
11
Q
Cos2A = 1 - 2square
Proof
A
- Use Cos2A = square - square
- cos^2 = (1-sin^2)
12
Q
Cos2A = 2square - 1 proof
A
- Use Cos2A = square - square
- sin^2 = (1-cos^2)
13
Q
Period of function
A
2pi / b
b is co-ef of x
Eg. Sin(3x)
Period is 2pi / 3
