
Identidades Pitagóricas
Presentation
•
Mathematics
•
10th Grade
•
Medium
Vanessa Sánchez
Used 14+ times
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7 Slides • 8 Questions
1
Identidades Pitagóricas
2
¿Por qué se denominan Identidades Pitagóricas?
Porque se aplica el teorema de Pitágoras con razones trigonométricas.
3
Recordemos el círculo unitario ó trigonométrico
Radio = 1 y la coordenada en términos de cos y sen
4
Mezclando el Teo. Pitágoras y el círculo trigonométrico tenemos:
sen2θ+cos2θ= 1
5
Multiple Choice
Se denominan identidades Pitagóricas porque:
Se aplica el Teorema de Tales
Se aplica el Teorema de Pitágoras
Pitágoras las bautizó así
6
Multiple Choice
La principal identidad pitagórica es:
sen2θ+cos2θ=−1
co2+ca2=1
sen2θ+cos2θ=1
7
Deducción de otra Pitagórica:
sen2θ+cos2θ=1
Dividimos la ecuación por sen2θ y tenemos:
sen2θsen2θ+sen2θcos2θ=sen2θ1
1+cot2θ=csc2θ
8
Multiple Choice
Al dividir sen2θ+cos2θ=1 entre cos2θ se obtiene:
cos2θsen2θ+cos2θcos2θ=cos2θ1
csc2θsen2θ+csc2θcot2θ=csc2θ1
9
Multiple Select
De cos2θsen2θ+cos2θcos2θ=cos2θ1 se obtiene:
cot2θ+1=sec2θ
tan2θ+1=sec2θ
tan2θ+1=csc2θ
10
Ejemplo de despeje:
sen2θ+cos2θ=1
sen2θ=1−cos2θ
11
Multiple Choice
Si se despeja cos2θ
de sen2θ+cos2θ=1 da como resultado:
1−sen2θ
1−cos2θ
1+sen2θ
12
Multiple Select
Si se despeja tan2θ de 1+tan2θ=sec2θ se obtiene:
sen2θ−1
sec2θ−1
sec2θ+1
13
Multiple Choice
Si se despeja cot2θ de 1+cot2θ=csc2θ se obtiene:
1−csc2θ
sec2θ−1
csc2θ−1
14
Ejemplo de aplicación
(1−senθ)(1+senθ)
Recordando la factorización a2−b2=(a−b)(a+b) tenemos:
12−sen2θ
cos2θ
15
Multiple Choice
(secθ−1)(secθ+1) se obtiene:
sec2θ−2=tan2θ
sec2θ−1=tan2θ
sec2θ−1=cot2θ
Identidades Pitagóricas
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