Trigonometric identities
Same angles:
Opposite angles:
and




Supplementary angles:
and




Complementary angles: and




Anti-supplementary angles: and




Table
f(x) | 0° | 30° | 45° | 60° | 90° |
---|---|---|---|---|---|
sin(A) | 0 | ![]() |
![]() |
![]() |
1 |
cos(A) | 1 | ![]() |
![]() |
![]() |
0 |
tan(A) | 0 | ![]() |
1 | ![]() |
und |
cot(A) | und | ![]() |
1 | ![]() |
0 |
Proof:
Angle sum and difference identities
Proof:

Remember that L²=(X2-X1)²+(Y2-Y1)²
The proof relies on the fact that W can be calculated 2 ways:
First way:
Second way:
put them together:
Left side:
Right side:
We can now clearly see that:
or