Mister Exam
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How to use it?
- Equation:
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Equation (x-1)(x+9)=8x
- Equation (49^sinx)^cosx=7^(sqrt3)^sinx
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Equation sin(6*x)+cos(6*x)*sqrt(3)=-2*cos(8*x)
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Equation k^2-5*k+6=0
- Express {x} in terms of y where:
- -1*x-19*y=-10
- 5*x+5*y=20
- 4*x-16*y=6
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
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Identical expressions
- sin(six *x)+cos(six *x)*sqrt(three)=- two *cos(eight *x)
- sinus of (6 multiply by x) plus co sinus of e of (6 multiply by x) multiply by square root of (3) equally minus 2 multiply by co sinus of e of (8 multiply by x)
- sinus of (six multiply by x) plus co sinus of e of (six multiply by x) multiply by square root of (three) equally minus two multiply by co sinus of e of (eight multiply by x)
- sin(6*x)+cos(6*x)*√(3)=-2*cos(8*x)
- sin(6x)+cos(6x)sqrt(3)=-2cos(8x)
- sin6x+cos6xsqrt3=-2cos8x
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Similar expressions
- sin6x+√3cos6x=-2cos8x.
- sin(6*x)-cos(6*x)*sqrt(3)=-2*cos(8*x)
- sin6x+3cos6x=-2cos8x
- sin(6*x)+cos(6*x)*sqrt(3)=+2*cos(8*x)
sin(6*x)+cos(6*x)*sqrt(3)=-2*cos(8*x) equation
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The solution
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___ sin(6*x) + cos(6*x)*\/ 3 = -2*cos(8*x)
$$\sin{\left(6 x \right)} + \sqrt{3} \cos{\left(6 x \right)} = - 2 \cos{\left(8 x \right)}$$
Detail solution
Given the equation:
$$\sin{\left(6 x \right)} + \sqrt{3} \cos{\left(6 x \right)} = - 2 \cos{\left(8 x \right)}$$
Transform
$$\sin{\left(6 x \right)} + \sqrt{3} \cos{\left(6 x \right)} + 2 \cos{\left(8 x \right)} = 0$$
$$4 \sin{\left(7 x + \frac{5 \pi}{12} \right)} \cos{\left(x + \frac{\pi}{12} \right)} = 0$$
Consider each factor separately
$$\cos{\left(x + \frac{\pi}{12} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(x + \frac{\pi}{12} \right)} = 0$$
This equation is transformed to
$$x + \frac{\pi}{12} = 2 \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x + \frac{\pi}{12} = 2 \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x + \frac{\pi}{12} = 2 \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{12} = 2 \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{12}$$
to right part of the equation with the opposite sign, in total:
$$x = 2 \pi n + \frac{5 \pi}{12}$$
$$x = 2 \pi n - \frac{7 \pi}{12}$$
$$\sin{\left(7 x + \frac{5 \pi}{12} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(7 x + \frac{5 \pi}{12} \right)} = 0$$
This equation is transformed to
$$7 x + \frac{5 \pi}{12} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$7 x + \frac{5 \pi}{12} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$7 x + \frac{5 \pi}{12} = 2 \pi n$$
$$7 x + \frac{5 \pi}{12} = 2 \pi n + \pi$$
, where n - is a integer
Move
$$\frac{5 \pi}{12}$$
to right part of the equation with the opposite sign, in total:
$$7 x = 2 \pi n - \frac{5 \pi}{12}$$
$$7 x = 2 \pi n + \frac{7 \pi}{12}$$
Divide both parts of the equation by
$$7$$
get the intermediate answer:
$$x = 2 \pi n + \frac{5 \pi}{12}$$
$$x = 2 \pi n - \frac{7 \pi}{12}$$
$$x = \frac{2 \pi n}{7} - \frac{5 \pi}{84}$$
$$x = \frac{2 \pi n}{7} + \frac{\pi}{12}$$
The final answer:
$$x_{1} = 2 \pi n + \frac{5 \pi}{12}$$
$$x_{2} = 2 \pi n - \frac{7 \pi}{12}$$
$$x_{3} = \frac{2 \pi n}{7} - \frac{5 \pi}{84}$$
$$x_{4} = \frac{2 \pi n}{7} + \frac{\pi}{12}$$
$$\sin{\left(6 x \right)} + \sqrt{3} \cos{\left(6 x \right)} = - 2 \cos{\left(8 x \right)}$$
Transform
$$\sin{\left(6 x \right)} + \sqrt{3} \cos{\left(6 x \right)} + 2 \cos{\left(8 x \right)} = 0$$
$$4 \sin{\left(7 x + \frac{5 \pi}{12} \right)} \cos{\left(x + \frac{\pi}{12} \right)} = 0$$
Consider each factor separately
Step
$$\cos{\left(x + \frac{\pi}{12} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(x + \frac{\pi}{12} \right)} = 0$$
This equation is transformed to
$$x + \frac{\pi}{12} = 2 \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x + \frac{\pi}{12} = 2 \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x + \frac{\pi}{12} = 2 \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{12} = 2 \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{12}$$
to right part of the equation with the opposite sign, in total:
$$x = 2 \pi n + \frac{5 \pi}{12}$$
$$x = 2 \pi n - \frac{7 \pi}{12}$$
Step
$$\sin{\left(7 x + \frac{5 \pi}{12} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(7 x + \frac{5 \pi}{12} \right)} = 0$$
This equation is transformed to
$$7 x + \frac{5 \pi}{12} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$7 x + \frac{5 \pi}{12} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$7 x + \frac{5 \pi}{12} = 2 \pi n$$
$$7 x + \frac{5 \pi}{12} = 2 \pi n + \pi$$
, where n - is a integer
Move
$$\frac{5 \pi}{12}$$
to right part of the equation with the opposite sign, in total:
$$7 x = 2 \pi n - \frac{5 \pi}{12}$$
$$7 x = 2 \pi n + \frac{7 \pi}{12}$$
Divide both parts of the equation by
$$7$$
get the intermediate answer:
$$x = 2 \pi n + \frac{5 \pi}{12}$$
$$x = 2 \pi n - \frac{7 \pi}{12}$$
$$x = \frac{2 \pi n}{7} - \frac{5 \pi}{84}$$
$$x = \frac{2 \pi n}{7} + \frac{\pi}{12}$$
The final answer:
$$x_{1} = 2 \pi n + \frac{5 \pi}{12}$$
$$x_{2} = 2 \pi n - \frac{7 \pi}{12}$$
$$x_{3} = \frac{2 \pi n}{7} - \frac{5 \pi}{84}$$
$$x_{4} = \frac{2 \pi n}{7} + \frac{\pi}{12}$$
The graph