Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)=sqrt(2)/2
-
Equation x+4/5-x/3=7
-
Equation 12x+5(6-3x)=10-3x
-
Equation x^2-x-20=0
- Express {x} in terms of y where:
- -11*x+4*y=-8
- -14*x+1*y=3
- 14*x+16*y=14
- 17*x-11*y=2
- Integral of d{x}:
-
cos^3x
- Derivative of:
-
cos^3x
-
Identical expressions
- cos^3x
- co sinus of e of cubed x
- cos3x
- cos³x
- cos to the power of 3x
cos^3x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos^{3}{\left(x \right)} = 0$$
transform
$$\cos^{3}{\left(x \right)} = 0$$
$$\cos^{3}{\left(x \right)} = 0$$
Do replacement
$$w = \cos{\left(x \right)}$$
Given the equation
$$w^{3} = 0$$
so
$$w = 0$$
We get the answer: w = 0
do backward replacement
$$\cos{\left(x \right)} = w$$
Given the equation
$$\cos{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
Or
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, where n - is a integer
substitute w:
$$x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x_{1} = \pi n + \frac{\pi}{2}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{2} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
$$x_{2} = \pi n - \frac{\pi}{2}$$
$$\cos^{3}{\left(x \right)} = 0$$
transform
$$\cos^{3}{\left(x \right)} = 0$$
$$\cos^{3}{\left(x \right)} = 0$$
Do replacement
$$w = \cos{\left(x \right)}$$
Given the equation
$$w^{3} = 0$$
so
$$w = 0$$
We get the answer: w = 0
do backward replacement
$$\cos{\left(x \right)} = w$$
Given the equation
$$\cos{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
Or
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, where n - is a integer
substitute w:
$$x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x_{1} = \pi n + \frac{\pi}{2}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{2} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
$$x_{2} = \pi n - \frac{\pi}{2}$$
Sum and product of roots
[src]
sum
pi 3*pi -- + ---- 2 2
$$\frac{\pi}{2} + \frac{3 \pi}{2}$$
=
2*pi
$$2 \pi$$
product
pi 3*pi --*---- 2 2
$$\frac{\pi}{2} \frac{3 \pi}{2}$$
=
2 3*pi ----- 4
$$\frac{3 \pi^{2}}{4}$$
3*pi^2/4
Rapid solution
[src]
pi
x1 = --
2
$$x_{1} = \frac{\pi}{2}$$
3*pi
x2 = ----
2
$$x_{2} = \frac{3 \pi}{2}$$
x2 = 3*pi/2
Numerical answer
[src]
x1 = 92.6768935770301
x2 = 23.5620444336803
x3 = 95.818627417042
x4 = -14.1371260033657
x5 = -73.827410994311
x6 = -64.4025554047934
x7 = 73.8274768053124
x8 = -83.2523004207065
x9 = 7.85402475701276
x10 = 20.4203112367381
x11 = -42.411405413931
x12 = -23.5619897288019
x13 = 1.5708945053691
x14 = -45.5531401844306
x15 = 51.8363261592826
x16 = 42.4114617473496
x17 = -36.1282768063468
x18 = -95.8185603030962
x19 = 26.7034598912501
x20 = 29.8451754771722
x21 = 48.6946439323886
x22 = 23.5619763533234
x23 = 45.553194340988
x24 = -86.3937054164085
x25 = 70.6857435758276
x26 = -29.8451152214988
x27 = 36.128317789764
x28 = -89.5354410428862
x29 = -61.2611644481175
x30 = 64.4026122770508
x31 = 92.6770059000324
x32 = -80.1105785507599
x33 = -61.2611560468397
x34 = -39.2700061565569
x35 = -58.1194276545353
x36 = -67.5442906223714
x37 = 58.1194603256925
x38 = 67.5443442271897
x39 = -7.85396939058216
x40 = 67.5443333859623
x41 = 70.6858302611407
x42 = 48.6945935926021
x43 = 4.71228651848371
x44 = -1.57083925518957
x45 = 26.7034436275456
x46 = -17.2788562472482
x47 = 89.5354940921686
x48 = 86.3937628262857
x49 = -51.8362625267018
x50 = -20.4202554438585
x51 = -20.4203505482106
x52 = -42.4114638604687
x53 = -92.6770895717702
x54 = 1.57080273224359
x55 = 80.1106035284868
x56 = -83.2523059178598
x57 = 4.71229368085888
x58 = 45.5531567451367
x59 = 14.1371748405436
x59 = 14.1371748405436