Find the simplified form of cos13/5 cos x 4/5 sin x, x ∈ 3π/4,π/4 asked in Class XII Maths by nikita74 ( 1,017 points) inverse trigonometric functions1/k 2 = π 2/6 P A short elementary proof of Daniel Daners∗ The University of Sydney, NSW 06, Australia danieldaners@sydneyeduau Revised version, Abstract P∞We give 2 a short elementary proof of the well known identity ζ(2) = 2 k=1 1/k = π /651 Approximating and Computing Area 3 2 25 3 35 4 45 5 5 10 15 25 30 x x 2x−2 2 25 3 35 4 45 5 5 10 15 x x x−2 6 Let f (x) = cos x (a) Calculate R 4 and L 4 for the interval 0, π 2 (b) Sketch the graph of f and the rectangles that make up each of the approximations (c) Is the area under the graph larger or smaller than R 4?ThanL 4?
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X 0 π 6 π 4 π 3 π 2 3 4 π π 3 2 π 2π yx=sin 0 05 2 2 ≈ 3 2 ≈ 1 2 2 ≈ 0 –1 0 yx=cos 1 3 2 ≈ 2 2 ≈ 05 0 −≈−2 2 –1 0 1 Now, if you plot these yvalues over the xvalues we have from the unwrapped unit circle, we get these graphsCosine calculator online cos(x) calculator This website uses cookies to improve your experience, analyze traffic and display adsThe solution of the equation sin1 6x sin1 6 √3 x = (π/2) is (A) (1/12) (B) 12 2 (D) (1/6) Check Answer and Solution for above q
π (6) Γ( )Γ( ) = Γ(x) 2 2 2x−1 The derivation and proof of these formulas can be found at 1 They are based on finding an approximation for Γ(x) in terms of an estimate for n!The number π (/ p aɪ /;Because of this the resulting boundary forces
7 Consider f (x) = 5x on 0,3 (aA most beautiful proof of the Basel problem, using lightHelp fund future projects https//wwwpatreoncom/3blue1brownAn equally valuable form of support isρ > 3 π G P 2 = 3 π 667 × 108 dyne cm 2 gm2 (13 s) 2 ≈ 10 8 g cm3 This limit is just consistent with the known densities of white dwarf stars But soon the faster ( P = 0033 s) pulsar in the Crab Nebula was discovered, and its period implies a
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Medium View solution The number of positive integral solutions of the equation(π)2 1− x2 (2π)2 1− x (3π)2 ··also has roots at x = 0,±π,±2π,±3π, Euler believed that these two functions are equivalent By Maclaurin series on sinx, we find that the coefficient of the x3 term = −1/6 On the other hand, for the infinite product, the coefficient of the x3 term = −I/π2 = − P∞ k=1 1/(k 2π2) ThusThe depth is modeled by the function D (t) = 5 sin (π 6 t − 7 π 6) 8, D (t) = 5 sin (π 6 t − 7 π 6) 8, where t t is the number of hours after midnight Find the rate at which the depth is changing at 6
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F0 changes from negative to positive at x = π/2 so, by the first derivative test, the local minimum value of f is f(π/2) = cos2(π/2)−2sin(π/2) = 02 −2(1) = −2 f0 changes from positive to negative at x = 3π/2 so, by the first derivative test, the local maximum value of f is =tan (4π/2π/6) clearly, the angle lies in IV quadrant in which tangent function is negative and the multiple of π/2 is even =tan (4π/2π/6)= cot (π/6) =1/√3 (iv) cos (25π/4) Solution The cosine function is an even function, Therefore, cos (25π/4)=cos (25π/4)3 THE PARTIAL FRACTION EXPANSION OF sin2 x The identity (6) is a special case (x = r/2) of 1 1 _ _N1 sin2 x N2 2 sin2xk7r (9) This identity follows for N = 2 n in the same way as in Section 1, starting from sin2 x Writing it as 1 = 1 N/21 1 N2 _L xk sin x N2 k n 22xsin yields the partial fraction expansion of sin2 x in the limit
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Transcript Ex 33, 3 Prove that cot2 π/6 cosec 5π/6 3 tan2 π/6 = 6 Taking LHS cot2 π/6 cosec 5π/6 3 tan2 π/6 Putting π = 180° = cot2(180/6) cosec((5 ×180)/6) 3 tan2(180/6) = cot2 30° cosec (150°) 3tan2 30° Here, tan 30° = 1/√3 cot 30° = 1/tan〖30°〗 = 1/(1/√3) = √3 For cosec 150° , First, Finding sin 150° sin 150° = sin (180 – 30° ) = sin 30Radians × (180/π) = Degrees Example 2 Convert π/6 into degrees Solution Using the formula, π/6 × (180/π) = 180/6 = 30 degrees Radian to Degree Equation As we know already, one complete revolution, counterclockwise, in an XY plane, will be equal to 2π (in radians) or 360° (in degrees) Therefore, both degree and radian can form an The maximum value of sin (x π/6) cos(x π/6) in the interval (0, π/2) is attained at (a) x = π/12 (b) x = π/6 (c) x = π/3 (d) x = π/2
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In Figure 6, notice that if one of the acute angles is labeled as θ, θ, then the other acute angle must be labeled (π 2 − θ) (π 2 − θ) Notice also that sin θ = cos (π 2 − θ), sin θ = cos (π 2 − θ), which is opposite over hypotenusePolygon Calculator Use this calculator to calculate properties of a regular polygon Enter any 1 variable plus the number of sides or the polygon name Calculates side length, inradius (apothem), circumradius, area and perimeter Calculate from an regular 3gon up to a regular 1000gon Units Note that units of length are shown for convenienceCalculate sec(π/6) Determine quadrant Since our angle is between 0 and π/2 radians, it is located in Quadrant I In the first quadrant, the values for sin, cos and tan are positive Determine angle type 0 is an acute angle since it is less than 90°
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3 Solution Since f(z) = ez has an antiderivative F(z) = ez everywhere in C, the integral is independent on the path and Z C ez dz = e3 2 πe i 3π 2 −e 2 e i π 2 = e−i3π 2 −ei π 2 = i−i = 0δ=−π/2 Hence, wave 1 is RHC Similarly, Ee 2 =xˆ 2e jkz yˆ 2e jkz e −jπ/2 Wave 2 has the same magnitude and phases as wave 1 except that its direction is along −ˆz instead of zˆ Hence, the locus of rotation of E will match the left hand instead of the right hand Thus, wave 2 is LHCSimplify (2pi)/ (pi/2) 2π π 2 2 π π 2 Multiply the numerator by the reciprocal of the denominator 2π 2 π 2 π 2 π Cancel the common factor of π π Tap for more steps Factor π π out of 2 π 2 π π ⋅ 2 2 π π ⋅ 2 2 π Cancel the common factor
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Spelled out as "pi") is a mathematical constant, approximately equal to It is defined in Euclidean geometry as the ratio of a circle's circumference to its diameter, and also has various equivalent definitionsThe number appears in many formulas in all areas of mathematics and physicsThe earliest known use of the Greek letter π to represent the ratio of aY x √ abs round N rand Measurements of pK a values, structural analyses, and computational studies revealed the presence of COOHπ interactions in 2,6diarylcarboxylic acids, 11 NHπ interactions in 2,6diarylpyridines, 12 cationπ interactions in 2,6diarylanilines, 13 and OHπ interactions in 2,6diarylphenols 10 Inspired by these precedents, here we report
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If tan − 1 a a x tan − 1 a a − x = 6 π , then x 2 =? ∴ f(x) is not strictly decreasing in any of the intervals (0, 1), (\(\frac { π }{ 2 }\), π) and (0, \(\frac { π }{ 2 }\)) Question 14 Find the least value of a such that the function f given by f (x) = x² ax 1 is strictly increasing on (1, 2)Click here👆to get an answer to your question ️ Prove cot pi24 = √(2) √(3) √(4) √(6) ?
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Question Find The Distance Between (2,π/6,0) And(1,π,2) , Where Points Are Given In Cylindrical Coordinatesans) 353 This problem has been solved!6003 Homework #10 Solutions / Fall 11 2 2 Inverse DT Fourier Series DeterminetheDTsignalswiththefollowingFourierseriescoefficients Assumethatthe1 rad = 180°/π = ° The angle α in degrees is equal to the angle α in radians times 180 degrees divided by pi constant α (degrees) = α (radians) × 180° / π or degrees = radians × 180° / π Example Convert 2 radians angle to degrees α (degrees) = α (radians) × 180° / π = 2 × 180° / = °
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5 EX 2 Convert the coordinates as indicated a) (8, π/4, π/6) from spherical to Cartesian b) (2√3, 6, 4) from Cartesian to spherical854 x 180/ π = 4502 degrees814 x 180/ π = – 4666 degrees π/180 x 180/ π = 1 degree Example 8 Convert the angle π /5 radians into degrees Solution Angle in radian x 180/ π = Angle in degrees By substitution, π /5 x 180/ π = 36 degrees Example 9 Convert the angle – π /8 radians into degrees SolutionThe Value of Cos 2 ( π 6 X ) − Sin 2 ( π 6 − X ) is CBSE CBSE (Arts) Class 11 Textbook Solutions 7909 Important Solutions 12 Question Bank Solutions 6916 Concept Notes & Videos 365 Syllabus Advertisement Remove all ads The Value of Cos 2 ( π 6 X ) − Sin 2 ( π 6 − X ) is
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2 π Z π 0 f(x)cosnxdx = 2 π Z π 0 xcosnx dx If n = 0, then a0 = 2 π Z π 0 x dx = π, and if n ≥ 1, then integrating by parts, one finds that 2 π Z π 0 xcosnx dx = 2 π xsinnx n − 2 nπ Z π 0 sinnx dx = 2 n2π cosnx π 0 = 2 n2π (−1)n − 1 Hence an = 0 if n is even and an = − 4 n2π when n is odd, and hence f(x) ∼ π 2The polar coordinates of a point are given Plot the point (6, π/2) 10 10 (6, π/2) (6, π/2) 10 5 10 10 10 10 6, /2) (6, π/2) 10 5 10 10 10 10L Find the corresponding rectangular coordinates for the point (x, y) = ( The polar coordinates of a point are given pi/6 radians is 30 degrees A radian is the angle subtended such that the arc formed is the same length as the radius There are 2pi radians in a circle, or 360 degrees Therefore, pi is equal to 180 degrees 180/6=30
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The benchmark angle measures (as defined by the College Board) are 0, ${π}/{6}$, ${π}/{4}$, ${π}/{3}$, ${π}/{2}$ radians which are equal to the angle measures 0°, 30°, 45°, 60°, and 90°, respectively You need to be able to use these with the trigonometric functions described in the above trigonometry section (sine, cosine, and tangentLet f(x) = 3sin^4x 10sin^3x 6sin^2x – 3, x ∈ π/6, π/2 then f is (1) increasing in (π/2, π/2) (2) decreasing in (0,π/2) ← Prev Question Next Question → 1 vote(511), in this case we obtain p ren i = δ iθ 8 π 2 ρ 3 bracketleftbigg 7 π 4 8 α 4 480 α 4 − parenleftbigg ξ − 1 6 parenrightbigg π 2 2 α 2 α 2 bracketrightbigg (522) We notice that also in this case the parameter ξ appears in the final expression for the renormalized pressure;
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Modified equations and π^2/6 Mats Vermeeren (TU Berlin) Numerical discretizations of differential equations are often studied through their modified equation This is a differential equation, usually obtained as a power series, with solutions that exactly interpolate the discretization2, 5 x = 0, 6 x = π 2, 7 x = π Toc JJ II J I Back Section 4 Integrals 17 4 Integrals Formula for integration by parts R b a udv dx dx = uv − 2 e^x (hyperbolic functions included), sin x, cos x, tan x all have a factorial in their power series The only useful examples I can think of that don't have a factorial are the inverse trig functions and the natural log Anyways, I don't want to get into an argument, I'll just rephrase myself, most power series that I've seen and
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1 2 3 π sin asin 4 5 6 − e cos acos exp ← 7 8 9 × g tan atan ln, • 0 E ∕ R rad deg log(a,b) ans; The beta function (also known as Euler's integral of the first kind) is important in calculus and analysis due to its close connection to the gamma function, which is itself a generalization of the factorial function Many complex integrals can be reduced to expressions involving the beta function The recurrence relation of the beta function is given by Transcript Ex 33, 2 Prove that 2sin2 π/6 cosec2 7π/6 cos2 π/3 = 3/2 Taking LHS 2sin2 π/6 cosec2 7π/6 cos2 π/3 Putting π = 180° = 2 sin2 180/6 cosec2 (7 ×180)/6 cos2 180/3 = 2sin2 30° cosec2 210° cos2 60° = 2(sin 30°)2 (cosec 210°)2 (cos 60°)2 Here, sin 30° = 1/2 & cos 60° = 1/2 For cosec 210° , lets first calculate sin 210° sin 210° = sin (180 30) = −sin
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