because the ratio of one side of a triangle to the hypotenuse can never be more that one.
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Sine(pi/2) = 1 This is 'Radian' measure of an angle. pi/2 radians = 90 degrees. When you see something like 'Sine(pi/2)' make sure your calculator is in RADIAN mode. ' NOT degree mode.
(1 - cos(2x))/2, where x is the variable. And/Or, 1 - cos(x)^2, where x is the variable.
A dot A = A2 do a derivative of both sides derivative (A) dot A + A dot derivative(A) =0 2(derivative (A) dot A)=0 (derivative (A) dot A)=0 A * derivative (A) * cos (theta) =0 => theta =90 A and derivative (A) are perpendicular
sin(x) = cos(x)sin(x)/cos(x) = tan(x) = 1x = arctan(1) = 45 degreessin(45)=cos(45) = Sqrt(2)/2 Answer: By observation. Since Sine = Opposite over hypotenuse and Cosine = Adjacent over hypotenuse. Any right angle triangle where the opposite and adjacent sides are the same length will have Sine equal to Cosine. This only happens with an isosceles triangle (two sides are equal in length). When one angle is 90o the other two are 45o.
To find the area of one cylinder you integrate over dh and dt (theta) like this: r.dt.dh with dt from 0 to 2pi radians. The intersection changes the limits of theta. Assuming that the center of the second cylinder is exactly R from the other cylinder then theta goes from 0 to 2pi*2/3. The 2/3 is because you have removed 120 degrees. However you now have two cylinders so you need to double it to: 2*2pi*2/3 which when factor in the height H and radius R gives you 8pi/3*R*H