Particular Values of Cosine Function
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Theorem
The following values of the cosine function can be expressed as exact algebraic numbers.
This list is non-exhaustive.
Cosine of Zero
- $\cos 0 = 1$
Cosine of 15 Degrees
- $\cos 15 \degrees = \cos \dfrac \pi {12} = \dfrac {\sqrt 6 + \sqrt 2} 4$
Cosine of 30 Degrees
- $\cos 30 \degrees = \cos \dfrac \pi 6 = \dfrac {\sqrt 3} 2$
Cosine of 45 Degrees
- $\cos 45 \degrees = \cos \dfrac \pi 4 = \dfrac {\sqrt 2} 2$
Cosine of 60 Degrees
- $\cos 60 \degrees = \cos \dfrac \pi 3 = \dfrac 1 2$
Cosine of 75 Degrees
- $\cos 75^\circ = \cos \dfrac {5 \pi}{12} = \dfrac {\sqrt 6 - \sqrt 2} 4$
Cosine of Right Angle
- $\cos 90 \degrees = \cos \dfrac \pi 2 = 0$
Cosine of 105 Degrees
- $\cos 105 \degrees = \cos \dfrac {7 \pi} {12} = - \dfrac {\sqrt 6 - \sqrt 2} 4$
Cosine of 120 Degrees
- $\cos 120 \degrees = \cos \dfrac {2 \pi} 3 = -\dfrac 1 2$
Cosine of 135 Degrees
- $\cos 135 \degrees = \cos \dfrac {3 \pi} 4 = -\dfrac {\sqrt 2} 2$
Cosine of 150 Degrees
- $\cos 150 \degrees = \cos \dfrac {5 \pi} 6 = -\dfrac {\sqrt 3} 2$
Cosine of 165 Degrees
- $\cos 165 \degrees = \cos \dfrac {11 \pi} {12} = - \dfrac {\sqrt 6 + \sqrt 2} 4$
Cosine of Straight Angle
- $\cos 180 \degrees = \cos \pi = -1$
Cosine of 195 Degrees
- $\cos 195 \degrees = \cos \dfrac {13 \pi} {12} = - \dfrac {\sqrt 6 + \sqrt 2} 4$
Cosine of 210 Degrees
- $\cos 210 \degrees = \cos \dfrac {7 \pi} 6 = -\dfrac {\sqrt 3} 2$
Cosine of 225 Degrees
- $\cos 225 \degrees = \cos \dfrac {5 \pi} 4 = -\dfrac {\sqrt 2} 2$
Cosine of 240 Degrees
- $\cos 240 \degrees = \cos \dfrac {4 \pi} 3 = -\dfrac 1 2$
Cosine of 255 Degrees
- $\cos 255^\circ = \cos \dfrac {17 \pi} {12} = - \dfrac {\sqrt 6 - \sqrt 2} 4$
Cosine of Three Right Angles
- $\cos 270 \degrees = \cos \dfrac {3 \pi} 2 = 0$
Cosine of 285 Degrees
- $\cos 285^\circ = \cos \dfrac {19 \pi} {12} = \dfrac {\sqrt 6 - \sqrt 2} 4$
Cosine of 300 Degrees
- $\cos 300 \degrees = \cos \dfrac {5 \pi} 3 = \dfrac 1 2$
Cosine of 315 Degrees
- $\cos 315 \degrees = \cos \dfrac {7 \pi} 4 = \dfrac {\sqrt 2} 2$
Cosine of 330 Degrees
- $\cos 330 \degrees = \cos \dfrac {11 \pi} 6 = \dfrac {\sqrt 3} 2$
Cosine of 345 Degrees
- $\cos 345 \degrees = \cos \dfrac {23 \pi} {12} = \dfrac {\sqrt 6 + \sqrt 2} 4$
Cosine of Full Angle
- $\cos 360 \degrees = \cos 2 \pi = 1$
Also see
- Particular Values of Sine Function
- Particular Values of Tangent Function
- Particular Values of Cotangent Function
- Particular Values of Secant Function
- Particular Values of Cosecant Function
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles