Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)=4
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Equation 5^x=125
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Equation (|x+4|)=5
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Equation 2*sin(x)=1
- Express {x} in terms of y where:
- 16*x-17*y=-15
- -4*x-4*y=19
- 15*x+1*y=19
- -5*x-2*y=9
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Identical expressions
- two +√2sin(x)= zero
- 2 plus √2 sinus of (x) equally 0
- two plus √2 sinus of (x) equally zero
- 2+√2sinx=0
- 2+√2sin(x)=O
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Similar expressions
- 2-√2sin(x)=0
- 2+√2sinx=0
2+√2sin(x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{2 \sin{\left(x \right)}} + 2 = 0$$
transform
$$\sqrt{2} \sqrt{\sin{\left(x \right)}} + 2 = 0$$
$$\sqrt{2 \sin{\left(x \right)}} + 2 = 0$$
Do replacement
$$w = \sin{\left(x \right)}$$
Given the equation
$$\sqrt{2} \sqrt{w} + 2 = 0$$
Because equation degree is equal to = 1/2 and the free term = -2 < 0,
so the real solutions of the equation d'not exist
do backward replacement
$$\sin{\left(x \right)} = w$$
Given the equation
$$\sin{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, where n - is a integer
substitute w:
$$\sqrt{2 \sin{\left(x \right)}} + 2 = 0$$
transform
$$\sqrt{2} \sqrt{\sin{\left(x \right)}} + 2 = 0$$
$$\sqrt{2 \sin{\left(x \right)}} + 2 = 0$$
Do replacement
$$w = \sin{\left(x \right)}$$
Given the equation
$$\sqrt{2} \sqrt{w} + 2 = 0$$
Because equation degree is equal to = 1/2 and the free term = -2 < 0,
so the real solutions of the equation d'not exist
do backward replacement
$$\sin{\left(x \right)} = w$$
Given the equation
$$\sin{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, where n - is a integer
substitute w: