Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+9=(x+9)^2
-
Equation 3*x+5+(x+5)=(1-x)+4
-
Equation 9x-7=6x+14
-
Equation (x-5)^2=(x+10)^2
- Express {x} in terms of y where:
- -18*x-1*y=-11
- 10*x+5*y=-17
- -2*x-14*y=7
- 7*x+13*y=-13
- Graphing y =:
- sqrt(cos(x)-1)
- Derivative of:
- sqrt(cos(x)-1)
-
Identical expressions
- sqrt(cos(x)- one)= zero
- square root of ( co sinus of e of (x) minus 1) equally 0
- square root of ( co sinus of e of (x) minus one) equally zero
- √(cos(x)-1)=0
- sqrtcosx-1=0
- sqrt(cos(x)-1)=O
-
Similar expressions
- sqrt(cos(x)+1)=0
- sqrt(cosx-1)=0
sqrt(cos(x)-1)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{\cos{\left(x \right)} - 1} = 0$$
transform
$$\sqrt{\cos{\left(x \right)} - 1} = 0$$
$$\sqrt{\cos{\left(x \right)} - 1} = 0$$
Do replacement
$$w = \cos{\left(x \right)}$$
Given the equation
$$\sqrt{w - 1} = 0$$
so
$$w - 1 = 0$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
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:
$$x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$x_{1} = \pi n$$
$$x_{2} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{2} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
$$x_{2} = \pi n - \pi$$
$$\sqrt{\cos{\left(x \right)} - 1} = 0$$
transform
$$\sqrt{\cos{\left(x \right)} - 1} = 0$$
$$\sqrt{\cos{\left(x \right)} - 1} = 0$$
Do replacement
$$w = \cos{\left(x \right)}$$
Given the equation
$$\sqrt{w - 1} = 0$$
so
$$w - 1 = 0$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
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:
$$x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$x_{1} = \pi n$$
$$x_{2} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{2} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
$$x_{2} = \pi n - \pi$$
Sum and product of roots
[src]
sum
2*pi
$$2 \pi$$
=
2*pi
$$2 \pi$$
product
0*2*pi
$$0 \cdot 2 \pi$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = 69.1150383789755
x2 = 12.5663706143592
x3 = -50.2654824574367
x4 = 25.1327412287183
x5 = 18.8495559215388
x6 = 56.5486677646163
x7 = 56.5486677646163
x8 = 94.2477796076938
x9 = 43.9822971502571
x10 = -69.1150383789755
x11 = -81.6814089933346
x12 = 50.2654824574367
x13 = 87.9645943005142
x14 = -43.9822971502571
x15 = -6.28318530717959
x16 = -502.654824574367
x17 = -18.8495559215388
x18 = 138.230076757951
x19 = 50.2654824574367
x20 = 81.6814089933346
x21 = -62.8318530717959
x22 = 6.28318530717959
x23 = -94.2477796076938
x24 = -12.5663706143592
x25 = 119.380520836412
x26 = 75.398223686155
x27 = -75.398223686155
x28 = -31.4159265358979
x29 = 62.8318530717959
x30 = -6.28318530717961
x31 = -56.5486677646163
x32 = -87.9645943005142
x33 = 37.6991118430775
x34 = -25.1327412287183
x35 = -37.6991118430775
x36 = 100.530964914873
x37 = 0.0
x38 = 31.4159265358979
x39 = 12.5663706143592
x40 = -100.530964914873
x40 = -100.530964914873
The graph