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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