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What is the sin pi over 2?
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.
Sine squared in terms of cosine?
(1 - cos(2x))/2, where x is the variable. And/Or, 1 - cos(x)^2, where x is the variable.
Prove that a constant vector always has a perpendicular derivative?
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
Show that sin x equals cos x for some angle t between 0 and 90?
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.
How do you use double integrals to find the surface area of two intersecting cylinders of radius 1?
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
