Cartesian Coordinate Systems - 3D Math Primer for Graphics and Game Development - page 25

θ o

θ rad cosθ sinθ tanθ secθ cscθ cotθ

0 0 1 0 0 1 undef undef

√

√ √

3
3

√

π
6

3
2

1
2

2 3

30 ≈ 0.5236 2 3

3

√ √

√ √

π
4

2
2

2

45 ≈ 0.7854 1 2 2 1

2

√

√ √ √

π
3

1
2

3 2 3 3

60 ≈ 1.0472 3 2

2 3 3

π
2

90 ≈ 1.5708 0 1 undef undef 1 0

− √

√ √

− √

2π
3

− 2

3 2 3 3

120 ≈ 2.0944 3 −2

2 3 3

− √

√

− √

√

3π
4

2 2

135 ≈ 2.3562 −1 2 2 −1

2 2

− √

− √ − √

√

5π
6

3 1

2

3
3

− 2

3

150 ≈ 2.6180 2 3

2 3

180 π ≈ 3.1416 −1 0 0 −1 undef undef

− √ − √

√
3
3

√

7π
6

3

− 2 − 2

3

210 ≈ 3.6652 −2 3

2 3

√ √

− √ − √

5π
4

2 2

2

225 ≈ 3.9270 1 − 2 − 2 −1

2

√

− √

√

− √

4π
3

− 2

3
2

− 2

3 3

240 ≈ 4.1888 3 −2

3 3

3π
2

270 ≈ 4.7124 0 −1 undef undef −1 0

− √ − √

√

− √

5π
3

1
2

3
2

− 2

3 3

300 ≈ 5.2360 3 2

3 3

√

− √

√

− √

7π
4

2
2

2
2

315 ≈ 5.4978 −1 2 2 −1

− √

√

− √

√

11π
6

3
2

− 2

3
3

2 3

330 ≈ 5.7596 −2 3

3

360 2π ≈ 6.2832 1 0 0 1 undef undef

Table 1.2. Common angles in degrees and radians, and the values of the principal trig
functions

Perhaps the most famous and basic identity concerning the right tri-
angle, one that most readers learned in their primary education, is the
Pythagorean theorem. It says that the sum of the squares of the two legs of
a right triangle is equal to the square of the hypotenuse. Or, more famously,
as shown in Figure 1.20,

a 2 + b 2 = c 2 .

Pythagorean theorem

By applying the Pythagorean theorem to the unit circle, one can deduce
the identities

Pythagorean identities

sin 2 θ + cos 2 θ = 1,

1 + tan 2 θ = sec 2 θ, 1 + cot 2 θ = csc 2 θ.