Sr Examen
¿Cómo vas a descomponer esta cos((17*pi)/2-1/(2*pi)) expresión en fracciones?
Solución
Ha introducido
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/17*pi 1 \ cos|----- - ----| \ 2 2*pi/
$$\cos{\left(- \frac{1}{2 \pi} + \frac{17 \pi}{2} \right)}$$
cos((17*pi)/2 - 1/(2*pi))
Descomposición de una fracción
[src]
sin(1/(2*pi))
$$\sin{\left(\frac{1}{2 \pi} \right)}$$
/ 1 \ sin|----| \2*pi/
Simplificación general
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/ 2\ |1 - 17*pi | cos|----------| \ 2*pi /
$$\cos{\left(\frac{1 - 17 \pi^{2}}{2 \pi} \right)}$$
cos((1 - 17*pi^2)/(2*pi))
Unión de expresiones racionales
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/ 2\ |-1 + 17*pi | cos|-----------| \ 2*pi /
$$\cos{\left(\frac{-1 + 17 \pi^{2}}{2 \pi} \right)}$$
cos((-1 + 17*pi^2)/(2*pi))
Denominador común
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/ 1 \ sin|----| \2*pi/
$$\sin{\left(\frac{1}{2 \pi} \right)}$$
sin(1/(2*pi))
Denominador racional
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/ 1 \ sin|----| \2*pi/
$$\sin{\left(\frac{1}{2 \pi} \right)}$$
sin(1/(2*pi))
Potencias
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/ 1 \ sin|----| \2*pi/
$$\sin{\left(\frac{1}{2 \pi} \right)}$$
/ 1 17*pi\ / 1 17*pi\
I*|---- - -----| I*|- ---- + -----|
\2*pi 2 / \ 2*pi 2 /
e e
----------------- + -------------------
2 2
$$\frac{e^{i \left(- \frac{17 \pi}{2} + \frac{1}{2 \pi}\right)}}{2} + \frac{e^{i \left(- \frac{1}{2 \pi} + \frac{17 \pi}{2}\right)}}{2}$$
exp(i*(1/(2*pi) - 17*pi/2))/2 + exp(i*(-1/(2*pi) + 17*pi/2))/2
Parte trigonométrica
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1 -------------- / 1 pi\ sec|---- - --| \2*pi 2 /
$$\frac{1}{\sec{\left(- \frac{\pi}{2} + \frac{1}{2 \pi} \right)}}$$
2/pi 1 \
-1 + tan |-- + ----|
\4 4*pi/
--------------------
2/pi 1 \
1 + tan |-- + ----|
\4 4*pi/
$$\frac{-1 + \tan^{2}{\left(\frac{1}{4 \pi} + \frac{\pi}{4} \right)}}{1 + \tan^{2}{\left(\frac{1}{4 \pi} + \frac{\pi}{4} \right)}}$$
/ 1 \
2*cot|----|
\4*pi/
--------------
2/ 1 \
1 + cot |----|
\4*pi/
$$\frac{2 \cot{\left(\frac{1}{4 \pi} \right)}}{1 + \cot^{2}{\left(\frac{1}{4 \pi} \right)}}$$
/ 1 \ sin|----| \2*pi/
$$\sin{\left(\frac{1}{2 \pi} \right)}$$
/ 1 \ sin|9*pi - ----| \ 2*pi/
$$\sin{\left(- \frac{1}{2 \pi} + 9 \pi \right)}$$
1 -------------- /pi 1 \ sec|-- - ----| \2 2*pi/
$$\frac{1}{\sec{\left(- \frac{1}{2 \pi} + \frac{\pi}{2} \right)}}$$
2/pi 1 \
1 - cot |-- + ----|
\4 4*pi/
-------------------
2/pi 1 \
1 + cot |-- + ----|
\4 4*pi/
$$\frac{1 - \cot^{2}{\left(\frac{1}{4 \pi} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{1}{4 \pi} + \frac{\pi}{4} \right)} + 1}$$
/ 1 \
2*tan|----|
\4*pi/
--------------
2/ 1 \
1 + tan |----|
\4*pi/
$$\frac{2 \tan{\left(\frac{1}{4 \pi} \right)}}{\tan^{2}{\left(\frac{1}{4 \pi} \right)} + 1}$$
1 --------- / 1 \ csc|----| \2*pi/
$$\frac{1}{\csc{\left(\frac{1}{2 \pi} \right)}}$$
1
1 - ---------------
2/pi 1 \
tan |-- + ----|
\4 4*pi/
-------------------
1
1 + ---------------
2/pi 1 \
tan |-- + ----|
\4 4*pi/
$$\frac{1 - \frac{1}{\tan^{2}{\left(\frac{1}{4 \pi} + \frac{\pi}{4} \right)}}}{\frac{1}{\tan^{2}{\left(\frac{1}{4 \pi} + \frac{\pi}{4} \right)}} + 1}$$
/ 1 pi\ cos|---- - --| \2*pi 2 /
$$\cos{\left(- \frac{\pi}{2} + \frac{1}{2 \pi} \right)}$$
1
-1 + ---------------
2/pi 1 \
cot |-- + ----|
\4 4*pi/
--------------------
1
1 + ---------------
2/pi 1 \
cot |-- + ----|
\4 4*pi/
$$\frac{-1 + \frac{1}{\cot^{2}{\left(\frac{1}{4 \pi} + \frac{\pi}{4} \right)}}}{1 + \frac{1}{\cot^{2}{\left(\frac{1}{4 \pi} + \frac{\pi}{4} \right)}}}$$
(-1 + cot(pi/4 + 1/(4*pi))^(-2))/(1 + cot(pi/4 + 1/(4*pi))^(-2))