Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 5-2(x-1)=4-x
-
Equation 3*9^(x-1/2)-7*6^x+3*4^(x+1)=0
-
Equation 12-x^2=11
-
Equation 3*x^2-3=0
- Express {x} in terms of y where:
- 20*x-4*y=-7
- -19*x-14*y=-8
- 1*x+4*y=20
- -2*x+1*y=-8
- Derivative of:
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sin(t)
- Limit of the function:
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sin(t)
-
sqrt(2)/2
- Integral of d{x}:
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sin(t)
- sqrt(2)/2
-
Identical expressions
- sin(t)=sqrt(two)/ two
- sinus of (t) equally square root of (2) divide by 2
- sinus of (t) equally square root of (two) divide by two
- sin(t)=√(2)/2
- sint=sqrt2/2
- sin(t)=sqrt(2) divide by 2
-
Similar expressions
- cos*((pi*(2*x+6))/4)=-(sqrt2/2)
- sint=-1/2
- sint=-0.2
sin(t)=sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(t \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$t = 2 \pi n + \frac{\pi}{4}$$
$$t = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
$$\sin{\left(t \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$t = 2 \pi n + \frac{\pi}{4}$$
$$t = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Rapid solution
[src]
pi
t1 = --
4
$$t_{1} = \frac{\pi}{4}$$
3*pi
t2 = ----
4
$$t_{2} = \frac{3 \pi}{4}$$
t2 = 3*pi/4
Sum and product of roots
[src]
sum
pi 3*pi -- + ---- 4 4
$$\frac{\pi}{4} + \frac{3 \pi}{4}$$
=
pi
$$\pi$$
product
pi 3*pi --*---- 4 4
$$\frac{\pi}{4} \frac{3 \pi}{4}$$
=
2 3*pi ----- 16
$$\frac{3 \pi^{2}}{16}$$
3*pi^2/16
Numerical answer
[src]
t1 = -43.1968989868597
t2 = 51.0508806208341
t3 = -74.6128255227576
t4 = 69.9004365423729
t5 = 8.63937979737193
t6 = -54.1924732744239
t7 = -80.8960108299372
t8 = 77.7544181763474
t9 = -186.139364725195
t10 = 2476.36040919215
t11 = 32.2013246992954
t12 = 33.7721210260903
t13 = 46.3384916404494
t14 = 71.4712328691678
t15 = -98.174770424681
t16 = -16.4933614313464
t17 = -85.6083998103219
t18 = -118.595122673015
t19 = 2.35619449019234
t20 = -91.8915851175014
t21 = 96.6039740978861
t22 = -55.7632696012188
t23 = 65.1880475619882
t24 = 27.4889357189107
t25 = 88.7499924639117
t26 = 19.6349540849362
t27 = -22.776546738526
t28 = 25.9181393921158
t29 = -30.6305283725005
t30 = -24.3473430653209
t31 = 101.316363078271
t32 = -3.92699081698724
t33 = 40.0553063332699
t34 = -79.3252145031423
t35 = 90.3207887907066
t36 = 57.3340659280137
t37 = -73.0420291959627
t38 = -36.9137136796801
t39 = 0.785398163397448
t40 = 58.9048622548086
t41 = -237.975643509427
t42 = -41.6261026600648
t43 = 63.6172512351933
t44 = -5.49778714378214
t45 = -18.0641577581413
t46 = -87.1791961371168
t47 = -62.0464549083984
t48 = -68.329640215578
t49 = -66.7588438887831
t50 = -60.4756585816035
t51 = 84.037603483527
t52 = 14.9225651045515
t53 = 82.4668071567321
t54 = 6964.12551484517
t55 = 13.3517687777566
t56 = -11.7809724509617
t57 = -35.3429173528852
t58 = 38.484510006475
t59 = 52.621676947629
t60 = 44.7676953136546
t61 = 7.06858347057703
t62 = 76.1836218495525
t63 = -47.9092879672443
t64 = 128.019900633784
t65 = 95.0331777710912
t66 = 21.2057504117311
t67 = -49.4800842940392
t68 = -93.4623814442964
t69 = 2151.20556954561
t70 = -10.2101761241668
t71 = -17680.09805624
t72 = -1160.03308733803
t73 = -99.7455667514759
t74 = -29.0597320457056
t74 = -29.0597320457056