1.5
square root 3/2
-cos(x) + constant
It is not totally clear to what the square root applies*; if just the 2, then: d/dx ((√2)sin x) = (√2) cos x if all of 2 sin x, then: d/dx (√(2 sin x)) = cos x / √(2 sin x) * for the second version I would expect "square root all of 2 sin x" but some people would write as given in the question meaning this, so I've given both just in case.
It would be 1 over square root 5.
sin(405) = square root of 2 divided by 2 which is about 0.7071067812
Do you mean sin(x)=sqrt(3)/2? IF so, look at at 30/60/90 triangle. We see the sin 60 degrees is square (root of 3)/2
1.5
cos A=3/5 sin=square root of (1-cos2) sin=square root of (1-3/52) sin=square root of (1-9/25) sin=square root of (16/25) sin=4/5 csc=1/sin csc=1/(4/5) csc=5/4
750
one over the square root of 2 or 0.850903525
sin-30 = (-1) x 1/(square root of 2) -sin30 = -(1/square root of 2) They are equal
Do sin(x), square it, and then multiply it by two.
The derivative of cos x is -sin x, the derivative of square root of x is 1/(2 root(x)). Applying the chain rule, the derivative of cos root(x) is -sin x times 1/(2 root(x)), or - sin x / (2 root x).
square root 3/2
1/square root 2
sin(1,305) = sin(225) = -0.70711 (rounded) = 1/2 of the negative square root of 2.