Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
-
Ecuación 5-x^2=0
- Expresar {x} en función de y en la ecuación:
- -17*x-12*y=-9
- 18*x+17*y=-14
- 14*x-10*y=-4
- -17*x-8*y=7
- Derivada de:
-
-sin^2x
-
Expresiones idénticas
- cos^2x+sinx=-sin^2x
- coseno de al cuadrado x más seno de x es igual a menos seno de al cuadrado x
- cos2x+sinx=-sin2x
- cos²x+sinx=-sin²x
- cos en el grado 2x+sinx=-sin en el grado 2x
-
Expresiones semejantes
- cos^2x+sinx=+sin^2x
- cos^2x-sinx=-sin^2x
-
Expresiones con funciones
- Coseno cos
- cos(2pi×x)-3sin(pi×x)+1=0
- cos(x+(|x|))=1
- cos(x-3/4)=0
- cos(x)=-0,7
- cos(y)=x-3
- Seno sin
- sin(x)-2*x-1=0
- sin(1)/((3*x))=-1
- sin(pi*(x^2+1)/(x^2+11))=1/2
- sin(x)-2sqrt(x)=0
- sin(4*a)+cos(2*a)+sin(2*a)*cos(2*a)=1
cos^2x+sinx=-sin^2x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 cos (x) + sin(x) = -sin (x)
$$\sin{\left(x \right)} + \cos^{2}{\left(x \right)} = - \sin^{2}{\left(x \right)}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(x \right)} + \cos^{2}{\left(x \right)} = - \sin^{2}{\left(x \right)}$$
cambiamos
$$\sin{\left(x \right)} + 1 = 0$$
$$\sin{\left(x \right)} + 1 = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = -1$$
Obtenemos la respuesta: w = -1
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$x_{1} = 2 \pi n - \frac{\pi}{2}$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
$$x_{2} = 2 \pi n + \frac{3 \pi}{2}$$
$$\sin{\left(x \right)} + \cos^{2}{\left(x \right)} = - \sin^{2}{\left(x \right)}$$
cambiamos
$$\sin{\left(x \right)} + 1 = 0$$
$$\sin{\left(x \right)} + 1 = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = -1$$
Obtenemos la respuesta: w = -1
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$x_{1} = 2 \pi n - \frac{\pi}{2}$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
$$x_{2} = 2 \pi n + \frac{3 \pi}{2}$$
Suma y producto de raíces
[src]
suma
-pi ---- 2
$$- \frac{\pi}{2}$$
=
-pi ---- 2
$$- \frac{\pi}{2}$$
producto
-pi ---- 2
$$- \frac{\pi}{2}$$
=
-pi ---- 2
$$- \frac{\pi}{2}$$
-pi/2
Respuesta numérica
[src]
x1 = -64.4026491641039
x2 = 73.8274268520838
x3 = -7.85398205280014
x4 = -39.2699069219675
x5 = -89.5353901118113
x6 = -39.2699084145515
x7 = 17.2787591562062
x8 = -20.4203520060805
x9 = -64.4026498988255
x10 = 23.5619451518571
x11 = -32.9867232184024
x12 = 54.9778718908148
x13 = -32.9867224188086
x14 = 80.1106130902139
x15 = -39.2699076683741
x16 = -89.5353906059052
x17 = 61.2610563112167
x18 = 23.5619444059921
x19 = 538.783139388541
x20 = 29.8451303231501
x21 = 86.3937978309099
x22 = 86.3937978869933
x23 = 98.9601690454399
x24 = -45.5530935911043
x25 = 67.5442408278864
x26 = -95.8185763308148
x27 = -51.8362791922783
x28 = 67.5442415586719
x29 = -83.2522042893833
x30 = 80.1106122287081
x31 = 92.6769843439965
x32 = -102.101761026058
x33 = -45.5530929624673
x34 = 10.9955739381756
x35 = 42.4115007162407
x36 = -51.8362786893284
x37 = 36.1283157235346
x38 = 4.71238874329685
x39 = 36.1283159497235
x40 = 48.6946870830469
x41 = -64.4026502975618
x42 = -26.7035372004893
x43 = -95.818575476176
x44 = -95.8185758680502
x45 = 29.845130330036
x46 = 4.71239022926564
x47 = 54.9778710948428
x48 = 17.2787599560783
x49 = 61.2610571125526
x50 = -58.1194639046052
x51 = -70.6858351534454
x52 = 92.6769837888103
x53 = -7.85398119154045
x54 = 48.6946866365921
x55 = -14.1371668370864
x56 = -70.6858331259916
x57 = -20.4203527465087
x58 = -51.8362783335234
x59 = 73.8274274830848
x60 = 29.8451297031011
x61 = -1.57079643188553
x62 = 48.6946873020308
x63 = 67.54424230971
x64 = 48.6946859012172
x65 = 10.9955747360645
x66 = -20.420353265929
x67 = 42.4115013353669
x68 = 36.1283150875497
x69 = 92.6769830592094
x70 = -76.9690203748894
x71 = -1.57079639503667
x72 = 86.3937984838325
x73 = -14.1371667858125
x74 = -1.57079581340397
x75 = -26.7035379986821
x76 = -89.535390750197
x77 = -70.6858343571487
x78 = 23.5619437708833
x79 = -45.5530935025548
x80 = -76.9690195738024
x81 = -83.2522055723275
x82 = 4.7123894841958
x83 = 42.4115007274741
x84 = 80.1106131368654
x85 = 73.8274274426229
x86 = 98.9601692809083
x87 = -58.1194639976905
x88 = -7.85398149665124
x89 = -83.2522048211133
x90 = 98.9601682515978
x91 = -58.1194645939029
x92 = -14.1371674455661
x92 = -14.1371674455661