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FORMULARIOS, TABLAS Y CONSTANTES DE MATEMÁTICAS
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TRIGONOMETRÍA |
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DEFINICIONES TRIGONOMÉTRICAS |
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GRADOS |
ÁNGULOS |
RADIÁN |
| Existen dos
sistemas: Sexagesimal ==>> DEG (modo calculadora) Un círculo = 360º 1º = 60' y 1' =60'' Centesimal ==>> GRA (modo calculadora) Un círculo = 400 g 1g =100 m y 1m = 100 s |
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El
radián es una unidad de ángulo. Se
define como el ángulo cuyo arco tiene el mismo valor que el radio. x = 1 rad => OC=AC Un círculo tiene 2π rad (6,28 aprox.) π rad = 180º = 200 g (equivalencia) |
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s BA sen x = — = —— r OA |
c OB cos x = — = —— r OA |
t CD sen x tg x = — = —— = ———— r OC cos x |
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1 OD' r cosec x = —— = —— = — sen x r s |
1 OD r sec x = —— = —— = — cos x r c |
1 C'D' cos x cotg x = — = —— = ——— tg x r sen x |
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Si r = 1 |
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| sen x = s | cos x = c | tg x = t |
| cosec x = OD' = s' | sec x = OD = c' | cotg x = C'D' = t' |
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FÓRMULAS FUNDAMENTALES |
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sen2 x + cos2 x = 1 |
sec2 x - tg2 x = 1 |
cosec2 x - cotg2 x = 1 |
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VALORES QUE PUEDEN TOMAR LAS RAZONES TRIGONOMÉTRICAS |
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-1≤ sen x ≤ 1 |
-1≤ cos x ≤ 1 |
-∞ ≤ tg x ≤ ∞ |
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{cosec x ≤ -1} U {cosec x ≥ -1} |
{sec x ≤ -1} U {sec x ≥ -1} |
-∞ ≤ cotg x ≤ ∞ |
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DEFINICIONES DE ÁNGULOS |
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| Radián (rad) | Ángulo cuyo arco es igual al radio | |
| Grados sexagesimales (deg) | Ángulo recto = 90º ; 1º = 60' ; 1' = 60'' | |
| Grados centesimales (gra) | Ángulo recto = 100 g ; 1g = 100 m ; 1m = 100 s | |
| VALORES DE LAS RAZONES TRIGONOMÉTRICAS | ||||||||||||||||
| grad | 0 | 30 | 45 | 60 | 90 | 120 | 135 | 150 | 180 | 210 | 225 | 240 | 270 | 300 | 315 | 330 |
| rad | 0 | π/6 | π/4 | π/3 | π/2 | 2π/3 | 3π/4 | 5π/6 | π | 7π/6 | 5π/4 | 4π/3 | 3π/2 | 5π/3 | 7π/4 | 11π/6 |
| sen |
— √0 —— 2 |
— √ 1 —— 2 |
— √ 2 —— 2 |
— √ 3 —— 2 |
— √ 4 —— 2 |
— √3 —— 2 |
— √2 —— 2 |
1 —— 2 |
0 |
- 1 —— 2 |
— -√ 2 —— 2 |
— -√ 3 —— 2 |
-1 |
— -√ 3 —— 2 |
— -√ 2 —— 2 |
- 1 —— 2 |
| cos |
— √ 4 —— 2 |
— √ 3 —— 2 |
— √ 2 —— 2 |
— √ 1 —— 2 |
— √ 0 —— 2 |
- 1 —— 2 |
— -√ 2 —— 2 |
— -√3 —— 2 |
-1 |
— -√ 3 —— 2 |
— -√ 2 —— 2 |
- 1 —— 2 |
0 |
1 —— 2 |
— √ 2 —— 2 |
— √ 3 —— 2 |
| tg | 0 |
— √ 3 —— 3 |
1 |
— √ 3 |
--- |
— -√3
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-1 |
— -√3 —— 3 |
0 |
— √ 3 —— 3 |
1 |
— √ 3
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--- |
— -√ 3
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-1 |
— -√ 3 —— 3 |
| REGLA MNEMOTÉCTICA | ||||||||||||||||
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RELACIONES TRIGONOMÉTRICAS |
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| VALOR DE |
EN FUNCIÓN DE: |
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| sen x | cos x | tg x | cotg x | sec x | cosec x | |
| sen x | 1 |
————— ±√ 1 - cos2 x |
tg x —————— ————— ±√ 1 + tg2 x |
1 —————— ————— ±√ 1 - cotg2x |
————— ±√sec2 x - 1 ——————— sec x |
1 ————— cosec x |
| cos x |
————— ±√ 1 - sen2 x |
1 |
1 —————— ———— ±√1 + tg2 x |
cotg x ——————— ————— ±√1 + cotg2x |
1 ————— sec x |
—————— ±√cosec2 x - 1 ———————— cosec x |
| tg x |
sen x ——————— ————— ±√ 1 - sen2 x |
————— ±√1 - cos2 x —————— cos x |
1 |
1 ————— cotg x |
————— ±√ sec2 x - 1 |
1 ——————— —————— ±√cosec2 x - 1 |
| cotg x |
————— ±√1 - sen2 x ——————— sen x |
cos x ——————— ————— ±√1 - cos2 x |
1 ———— tg x |
1 |
1 ————— ———— ±√sec2 x -1 |
—————— ±√ cosec2 x - 1 |
| sec x |
1 ——————— ————— ±√ 1 - sen2 x |
1 ————— cos x |
————— ±√1 + tg2 x |
—————— ±√ 1 + cotg2x ———————— cotg x |
1 |
cosec x ——————— —————— ±√ cosec2 x - 1 |
| cosec x |
1 ————— sen x |
1 ——————— ————— ±√ 1 - cos2 x |
————— ±√1 + tg2 x ——————— tg x |
—————— ±√ 1 + cotg2x |
sec x —————— ————— ±√ sec2 x -1 |
1 |
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