Trigonometry
- 180° = π radians
- arc length = rθ when θ is in
radians
- area of sector =
- trigonometric equations have multiple solutions
- find the solutions in a given range i.e. 0
≤ x ≤ 360°
Degrees to radians conversion table
(Degrees / 180) * π =
radians i.e. 225°/180 = 1.25
1.25 * π = 1.25π = 5π/4
|
0° |
0/4 π |
0/2 π |
0 |
|
45° |
1/4 π |
|
π/4 |
|
90° |
2/4 π |
1/2 π |
π/2 |
|
135° |
3/4 π |
|
3π/4 |
|
180° |
4/4 π |
2/2 π |
π |
|
225° |
5/4 π |
|
5π/4 |
|
270° |
6/4 π |
3/2 π |
3π/2 |
|
315° |
7/4 π |
|
7π/4 |
|
360° |
8/4 π |
4/2 π |
2π |
Pythagorean identities
- SOH CAH TOA
- If you get given
, you can rewrite it in exact form. Draw a triangle.
Sine rule
Cosine rule
|
|
30 or π/6 |
45 or π/4 |
60 or π/3 |
|
sin |
0.5 |
1 / Ö2 |
Ö3 / 2 |
|
cos |
Ö3 / 2 |
1 / Ö2 |
0.5 |
|
tan |
1 / Ö3 |
1 |
Ö3 |
a = amplitude
(maximum height above centre of
oscillation)
= period (Where period is normally 1. Substitute 360° or
2π radians for 1 here)
c = horizontal translation to
the left
d = vertical translation of
centre of oscillation above the line y = 0