Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 0*x=0
-
Equation cos(x)=-1
-
Equation 3x-2=5
-
Equation 9-4x=3x-40
- Express {x} in terms of y where:
- -6*x+1*y=14
- -16*x-2*y=4
- sin(xy)+cos(xy)=tg(x+y)
- -17*x+13*y=-3
- Derivative of:
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tgt
-
-1
- Sum of series:
-
-1
- Integral of d{x}:
-
-1
-
Identical expressions
- tgt=- one
- tgt equally minus 1
- tgt equally minus one
-
Similar expressions
- x=2(cost+ln(tg(t/2)))
- arctg(t)
- tgt=+1
- tg(t)=6
tgt=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(t \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$t = \pi n - \frac{\pi}{4}$$
, where n - is a integer
$$\tan{\left(t \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$t = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-pi ---- 4
$$- \frac{\pi}{4}$$
=
-pi ---- 4
$$- \frac{\pi}{4}$$
product
-pi ---- 4
$$- \frac{\pi}{4}$$
=
-pi ---- 4
$$- \frac{\pi}{4}$$
-pi/4
Numerical answer
[src]
t1 = -101.316363078271
t2 = -88.7499924639117
t3 = 8.63937979737193
t4 = 99.7455667514759
t5 = -54.1924732744239
t6 = 77.7544181763474
t7 = 36.9137136796801
t8 = -25.9181393921158
t9 = 33.7721210260903
t10 = 46.3384916404494
t11 = -38.484510006475
t12 = 68.329640215578
t13 = 74.6128255227576
t14 = -63.6172512351933
t15 = -98.174770424681
t16 = -16.4933614313464
t17 = -85.6083998103219
t18 = 96.6039740978861
t19 = 2.35619449019234
t20 = -91.8915851175014
t21 = 71.4712328691678
t22 = 65.1880475619882
t23 = 27.4889357189107
t24 = -22.776546738526
t25 = 11.7809724509617
t26 = 55.7632696012188
t27 = -13.3517687777566
t28 = -3.92699081698724
t29 = 40.0553063332699
t30 = -79.3252145031423
t31 = 90.3207887907066
t32 = -73.0420291959627
t33 = 93.4623814442964
t34 = 30.6305283725005
t35 = -82.4668071567321
t36 = -95.0331777710912
t37 = 49.4800842940392
t38 = -0.785398163397448
t39 = 5.49778714378214
t40 = -41.6261026600648
t41 = 87.1791961371168
t42 = -76.1836218495525
t43 = 18.0641577581413
t44 = -44.7676953136546
t45 = -66.7588438887831
t46 = -60.4756585816035
t47 = 84.037603483527
t48 = 14.9225651045515
t49 = -35.3429173528852
t50 = 43.1968989868597
t51 = -19.6349540849362
t52 = 62.0464549083984
t53 = 80.8960108299372
t54 = -47.9092879672443
t55 = -32.2013246992954
t56 = 24.3473430653209
t57 = 21.2057504117311
t58 = -10.2101761241668
t59 = -51.0508806208341
t60 = -7.06858347057703
t61 = -69.9004365423729
t62 = 58.9048622548086
t63 = 52.621676947629
t64 = -57.3340659280137
t65 = -29.0597320457056
t65 = -29.0597320457056