Mister Exam
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How to use it?
- Equation:
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Equation 2*x^2+18*x=0
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Equation (x^2-9)^2+(x^2+x-6)^2=0
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Equation cos(x-pi/2)=0
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Identical expressions
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Similar expressions
- cos(x+pi/2)=0
cos(x-pi/2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x - \frac{\pi}{2} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(x - \frac{\pi}{2} \right)} = 0$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$x = 2 \pi n$$
$$x = 2 \pi n + \pi$$
, where n - is a integer
$$\cos{\left(x - \frac{\pi}{2} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\cos{\left(x - \frac{\pi}{2} \right)} = 0$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$x = 2 \pi n$$
$$x = 2 \pi n + \pi$$
, where n - is a integer
Numerical answer
[src]
x1 = 69.1150383789755
x2 = -97.3893722612836
x3 = 72.2566310325652
x4 = -40.8407044966673
x5 = -78.5398163397448
x6 = -3.14159265358979
x7 = 25.1327412287183
x8 = 18.8495559215388
x9 = 56.5486677646163
x10 = -50.2654824574367
x11 = 94.2477796076938
x12 = 34.5575191894877
x13 = -81.6814089933346
x14 = -69.1150383789755
x15 = 50.2654824574367
x16 = -267.035375555132
x17 = -232.477856365645
x18 = 43.9822971502571
x19 = 84.8230016469244
x20 = -34.5575191894877
x21 = 9.42477796076938
x22 = 65.9734457253857
x23 = 87.9645943005142
x24 = -53.4070751110265
x25 = 40.8407044966673
x26 = -113.097335529233
x27 = -43.9822971502571
x28 = -84.8230016469244
x29 = -6.28318530717959
x30 = -15.707963267949
x31 = -9.42477796076938
x32 = -18.8495559215388
x33 = 81.6814089933346
x34 = -62.8318530717959
x35 = 15.707963267949
x36 = 6.28318530717959
x37 = 28.2743338823081
x38 = -94.2477796076938
x39 = -12.5663706143592
x40 = 21.9911485751286
x41 = -47.1238898038469
x42 = 75.398223686155
x43 = -75.398223686155
x44 = -91.106186954104
x45 = 62.8318530717959
x46 = -31.4159265358979
x47 = -56.5486677646163
x48 = 3.14159265358979
x49 = 47.1238898038469
x50 = 78.5398163397448
x51 = 53.4070751110265
x52 = -87.9645943005142
x53 = 37.6991118430775
x54 = -72.2566310325652
x55 = 91.106186954104
x56 = -25.1327412287183
x57 = 59.6902604182061
x58 = 100.530964914873
x59 = -28.2743338823081
x60 = -2642.07942166902
x61 = -37.6991118430775
x62 = 0.0
x63 = -65.9734457253857
x64 = -21.9911485751286
x65 = 31.4159265358979
x66 = 12.5663706143592
x67 = -100.530964914873
x68 = 97.3893722612836
x69 = -59.6902604182061
x69 = -59.6902604182061
The graph