It is an anticlockwise rotation through 90 degrees.
180 degrees in the plane perpendicular to the xy plane. In general, no rotation in the (x, y) plane will take it to (-x, y) unless x = y (or -y) and, in that case it is a 270 degree clockwise rotation.
(x; y) --> (x.cos45 + y.sin45; x.sin45 - y.cos45)
Short answer: 72 degrees Longer answer: To rotate a star until it looks the same you need to make 1/5 of a complete 360 degree turn (since a star has 5 points). Sice 1/5 X 360 = 72, the answer is 72 degree angle rotation.
Suppose you wish to differentiate x/f(x) where f(x) is a differentiable function of x, and writing f for f(x) and f'(x) for the derivative of f(x), d/dx (x/f) = [f - x*f']/(f2)
You will need a good math app and scientific calculation.
follow this formula (x,y)->(-y,x)
It is an anticlockwise rotation through 90 degrees.
Yes. The transformation from y = f(x) to y=f(2x) will compress the shape along the x-axis by a factor of 2.
In two dimensions, the equations of rotation about the origin are: x' = x cos t - y sin t y' = x sin t + y cos t. where t is the angle of rotation, counterclockwise.
180 degrees in the plane perpendicular to the xy plane. In general, no rotation in the (x, y) plane will take it to (-x, y) unless x = y (or -y) and, in that case it is a 270 degree clockwise rotation.
The transformation from y = f(x) to y = f(x - 4) - 2
depends on the centre of rotation if it's about the origin the x coord is multiplied by -1
shown on graphs . 3 types : translation , rotaation , reflection x , y - -x ,y = reflection over y axis x,y- y,-x = reflection over x- axis translation= x,y - x+ or - horizontal change , y+ or - vertical change Perfect reflection= x,y - y,-x 180 degree rotation = x,y - -x , -y 90 degree clockwise rotation=x,y - y , -x 90 degree counter clockwise rotation = x,y - -y,x when graphing transformations , label the new image points as primes . When theres more then one prime , up the amount. Ex: A(1,0) becomes A'(A prime) (-1,0) hope this helps!
(x,y) to (x,-y). You would keep the x the same, but turn the y negative. This is actually the rule for a 90 degree counterclockwise rotation, but they're the same thing, they would go to the same coordinates.
(x,y) to (x,-y). You would keep the x the same, but turn the y negative. This is actually the rule for a 90 degree counterclockwise rotation, but they're the same thing, they would go to the same coordinates.
You have to add on the number that you want to transform the graph by. For example to move the graph 2 units along the x-axis the transformation would be f(x+2).