Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+9=(x+9)^2
-
Equation cos(x)=-1
-
Equation 3*x+50=77
-
Equation 5-2(x-1)=4-x
- Express {x} in terms of y where:
- 10*x+5*y=-17
- 14*x+16*y=-3
- -19*x+1*y=0
- 10*x+18*y=6
- Derivative of:
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cos(x)
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
-
Identical expressions
- cos(x)=- three / four
- co sinus of e of (x) equally minus 3 divide by 4
- co sinus of e of (x) equally minus three divide by four
- cosx=-3/4
- cos(x)=-3 divide by 4
-
Similar expressions
- (2x-3)/4+(x+2)/2=6+(2x-3)/2
- (5/12)*x-(3/4)=1/2
- cos(x)=+3/4
- cos(x/3)=0
- (x+3)/12-1*(x-3)/4=(x+2)/6
- cos(x/2)=-(1/2)
- cosx=-3/4
cos(x)=-3/4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = - \frac{3}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = - \frac{3}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-acos(-3/4) + 2*pi + acos(-3/4)
$$\operatorname{acos}{\left(- \frac{3}{4} \right)} + \left(- \operatorname{acos}{\left(- \frac{3}{4} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(-3/4) + 2*pi)*acos(-3/4)
$$\left(- \operatorname{acos}{\left(- \frac{3}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
=
(-acos(-3/4) + 2*pi)*acos(-3/4)
$$\left(- \operatorname{acos}{\left(- \frac{3}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
(-acos(-3/4) + 2*pi)*acos(-3/4)
Rapid solution
[src]
x1 = -acos(-3/4) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(- \frac{3}{4} \right)} + 2 \pi$$
x2 = acos(-3/4)
$$x_{2} = \operatorname{acos}{\left(- \frac{3}{4} \right)}$$
x2 = acos(-3/4)
Numerical answer
[src]
x1 = 52.6843408632131
x2 = -58.9675261703927
x3 = -46.4011555560335
x4 = 96.6666380134702
x5 = 14.9852290201356
x6 = 47.8466240516603
x7 = -52.6843408632131
x8 = -40.1179702488539
x9 = 90.3834527062906
x10 = -21.2684143273151
x11 = -84.100267399111
x12 = 105094.976306292
x13 = -54.1298093588399
x14 = 123.244847737815
x15 = -22.713882822942
x16 = 46.4011555560335
x17 = 3.86432690140321
x18 = 77.8170820919314
x19 = -16.4306975157624
x20 = 2.41885840577638
x21 = -98.112106509097
x22 = 71.5338967847518
x23 = -41.5634387444807
x24 = -72.9793652803787
x25 = -77.8170820919314
x26 = 58.9675261703927
x27 = 84.100267399111
x28 = 21.2684143273151
x29 = -96.6666380134702
x30 = -66.6961799731991
x31 = 27.5515996344947
x32 = 60.4129946660195
x33 = -35.2802534373011
x34 = -8.70204371295596
x35 = 385.693162143731
x36 = -27.5515996344947
x37 = -33.8347849416743
x38 = 28.9970681301216
x39 = 22.713882822942
x40 = 16.4306975157624
x41 = -65.2507114775722
x42 = 91.8289212019174
x43 = -91.8289212019174
x44 = 8.70204371295596
x45 = -28.9970681301216
x46 = -60.4129946660195
x47 = -3.86432690140321
x48 = 40.1179702488539
x49 = 35.2802534373011
x50 = -14.9852290201356
x51 = 79.2625505875583
x52 = 41.5634387444807
x53 = 98.112106509097
x54 = 54.1298093588399
x55 = -71.5338967847518
x56 = 10.1475122085828
x57 = 72.9793652803787
x58 = -79.2625505875583
x59 = -2.41885840577638
x60 = 65.2507114775722
x61 = -90.3834527062906
x62 = 33.8347849416743
x63 = -10.1475122085828
x64 = 85.5457358947378
x65 = -47.8466240516603
x66 = 66.6961799731991
x67 = -85.5457358947378
x67 = -85.5457358947378
The graph