Y Sin X. Calculus Integral with adjustable bounds example Calculus Fundamental Theorem of Calculus.
PDF filesin(x+ y) = sinxcosy+ cosxsiny sin(x y) = sinxcosy cosxsiny cos(x+ y) = cosxcosy sinxsiny cos(x y) = cosxcosy+ sinxsiny tan(x+ y) = tanx+tany 1 tanxtany tan(x y) = tanx tany 1+tanxtany HalfAngle Formulas sin 2 = q 1 cos 2 cos 2 = q 1+cos 2 tan 2 = q 1+cos tan 2 = 1 cosx sinx tan 2 = sin 1+cos DoubleAngle Formulas sin2 = 2sin cos cos2 = cos2 sin2 tan2 = 2tan 1 tan2.
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A specialty in mathematical expressions is that the multiplication sign can be left out sometimes for example we write “5x” instead of “5*x” The Derivative Calculator has to detect these cases and insert the multiplication sign The parser is implemented in JavaScript based on the Shuntingyard algorithm and can run directly in the browser.
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The “a” in the expression y = a sin x represents the amplitude of the graph It is an indication of how much energy the wave contains The amplitude is the distance from the “resting” position (otherwise known as the mean value or average value) of the curve In the interactive above the amplitude can be varied from `10` to `100` units.
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sin (x – y) = sin x cos y – cos x sin y sin (60° – 30°) = sin 60° cos 30° – cos 60° sin 30° sin (30°) = (√3/2) × (√3/2) + (1/2) × (1/2) 1/2 = 3/4 – 1/4 1/2 = 2/4 1/2 = 1/2 Hence verified cos (x + y) = cos x cos y – sin x sin y cos (60° + 30°) = cos 60° cos 30° – sin 60° sin 30°.
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Shifting angle by π/2 π 3π/2 (CoFunction Identities or Periodicity Identities) sin (π/2 – x) = cos x cos (π/2 – x) = sin x sin (π/2 + x) = cos x cos (π/2 + x) = – sin x sin (3π/2 – x) = – cos x cos (3π/2 – x) = – sin x sin (3π/2 + x) = – cos x.