Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation (4*cos(2*x)-9*sin(x)-4)/(sqrt(-cos(x)))=0
-
Equation 16x+9-4x^2=0
- Equation cos^2((2*pi/3)-x)=cos^2((2*pi/3)+x)
- Equation (x^2-16)^2+(x^2-3x-28)^2=0
- Express {x} in terms of y where:
- 5*x-5*y=20
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
-
Identical expressions
- (four *cos(two *x)- nine *sin(x)- four)/(sqrt(-cos(x)))= zero
- (4 multiply by co sinus of e of (2 multiply by x) minus 9 multiply by sinus of (x) minus 4) divide by ( square root of ( minus co sinus of e of (x))) equally 0
- (four multiply by co sinus of e of (two multiply by x) minus nine multiply by sinus of (x) minus four) divide by ( square root of ( minus co sinus of e of (x))) equally zero
- (4*cos(2*x)-9*sin(x)-4)/(√(-cos(x)))=0
- (4cos(2x)-9sin(x)-4)/(sqrt(-cos(x)))=0
- 4cos2x-9sinx-4/sqrt-cosx=0
- (4*cos(2*x)-9*sin(x)-4)/(sqrt(-cos(x)))=O
- (4*cos(2*x)-9*sin(x)-4) divide by (sqrt(-cos(x)))=0
-
Similar expressions
- (4*cos(2*x)-9*sin(x)+4)/(sqrt(-cos(x)))=0
- (4*cos(2*x)-9*sin(x)-4)/(sqrt(cos(x)))=0
- (4*cos(2*x)+9*sin(x)-4)/(sqrt(-cos(x)))=0
- (4*cos(2*x)-9*sinx-4)/(sqrt(-cosx))=0
(4*cos(2*x)-9*sin(x)-4)/(sqrt(-cos(x)))=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
4*cos(2*x) - 9*sin(x) - 4
------------------------- = 0
_________
\/ -cos(x)
$$\frac{\left(- 9 \sin{\left(x \right)} + 4 \cos{\left(2 x \right)}\right) - 4}{\sqrt{- \cos{\left(x \right)}}} = 0$$
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
x2 = pi
$$x_{2} = \pi$$
/ 2\
|/ ____\ |
|\9 - \/ 17 / |
I*log|-------------|
pi \ 64 /
x3 = - -- - --------------------
2 2
$$x_{3} = - \frac{\pi}{2} - \frac{i \log{\left(\frac{\left(9 - \sqrt{17}\right)^{2}}{64} \right)}}{2}$$
/ 2\
|/ ____\ |
|\9 + \/ 17 / |
I*log|-------------|
pi \ 64 /
x4 = - -- - --------------------
2 2
$$x_{4} = - \frac{\pi}{2} - \frac{i \log{\left(\frac{\left(\sqrt{17} + 9\right)^{2}}{64} \right)}}{2}$$
x4 = -pi/2 - i*log((sqrt(17) + 9)^2/64)/2
Sum and product of roots
[src]
sum
/ 2\ / 2\
|/ ____\ | |/ ____\ |
|\9 - \/ 17 / | |\9 + \/ 17 / |
I*log|-------------| I*log|-------------|
pi \ 64 / pi \ 64 /
pi + - -- - -------------------- + - -- - --------------------
2 2 2 2
$$\left(- \frac{\pi}{2} - \frac{i \log{\left(\frac{\left(\sqrt{17} + 9\right)^{2}}{64} \right)}}{2}\right) + \left(\pi + \left(- \frac{\pi}{2} - \frac{i \log{\left(\frac{\left(9 - \sqrt{17}\right)^{2}}{64} \right)}}{2}\right)\right)$$
=
/ 2\ / 2\
|/ ____\ | |/ ____\ |
|\9 + \/ 17 / | |\9 - \/ 17 / |
I*log|-------------| I*log|-------------|
\ 64 / \ 64 /
- -------------------- - --------------------
2 2
$$- \frac{i \log{\left(\frac{\left(\sqrt{17} + 9\right)^{2}}{64} \right)}}{2} - \frac{i \log{\left(\frac{\left(9 - \sqrt{17}\right)^{2}}{64} \right)}}{2}$$
product
/ / 2\\ / / 2\\
| |/ ____\ || | |/ ____\ ||
| |\9 - \/ 17 / || | |\9 + \/ 17 / ||
| I*log|-------------|| | I*log|-------------||
| pi \ 64 /| | pi \ 64 /|
0*pi*|- -- - --------------------|*|- -- - --------------------|
\ 2 2 / \ 2 2 /
$$0 \pi \left(- \frac{\pi}{2} - \frac{i \log{\left(\frac{\left(9 - \sqrt{17}\right)^{2}}{64} \right)}}{2}\right) \left(- \frac{\pi}{2} - \frac{i \log{\left(\frac{\left(\sqrt{17} + 9\right)^{2}}{64} \right)}}{2}\right)$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = -97.3893722612836
x2 = -43.9822971502571
x3 = -95.8185759344887 - 0.494932923094527*i
x4 = -78.5398163397448
x5 = 56.5486677646163
x6 = 28.2743338823081
x7 = -81.6814089933346
x8 = -15.707963267949
x9 = 72.2566310325652
x10 = -53.4070751110265
x11 = -106.814150222053
x12 = -18.8495559215388
x13 = -39.2699081698724 + 0.494932923094527*i
x14 = 50.2654824574367
x15 = 25.1327412287183
x16 = 100.530964914873
x17 = -9.42477796076938
x18 = 81.6814089933346
x19 = 69.1150383789755
x20 = -21.9911485751286
x21 = 53.4070751110265
x22 = -91.106186954104
x23 = -72.2566310325652
x24 = 15.707963267949
x25 = 40.8407044966673
x26 = -28.2743338823081
x27 = -62.8318530717959
x28 = -6.28318530717959
x29 = 3.14159265358979
x30 = -75.398223686155
x31 = -25.1327412287183
x32 = -7.85398163397448 - 0.494932923094527*i
x33 = -84.8230016469244
x34 = 42.4115008234622 + 0.494932923094527*i
x35 = 59.6902604182061
x36 = 36.1283155162826 - 0.494932923094527*i
x37 = -87.9645943005142
x38 = -34.5575191894877
x39 = -51.8362787842316 - 0.494932923094527*i
x40 = 31.4159265358979
x41 = 0.0
x42 = -65.9734457253857
x43 = 47.1238898038469
x44 = 18.8495559215388
x45 = 84.8230016469244
x46 = 91.106186954104
x47 = 6.28318530717959
x48 = -1.5707963267949 - 0.494932923094527*i
x49 = -47.1238898038469
x50 = 94.2477796076938
x51 = 65.9734457253857
x52 = -56.5486677646163
x53 = 21.9911485751286
x54 = 80.1106126665397 - 0.494932923094527*i
x55 = 78.5398163397448
x56 = 75.398223686155
x57 = 87.9645943005142
x58 = 12.5663706143592
x59 = -3.14159265358979
x60 = -37.6991118430775
x61 = -12.5663706143592
x62 = 97.3893722612836
x63 = -100.530964914873
x64 = 43.9822971502571
x65 = -50.2654824574367
x66 = 37.6991118430775
x67 = -40.8407044966673
x68 = -59.6902604182061
x69 = -69.1150383789755
x70 = 9.42477796076938
x71 = 62.8318530717959
x72 = -94.2477796076938
x73 = 34.5575191894877
x74 = -31.4159265358979
x74 = -31.4159265358979