For the complex numbers z = 30 (cosine (StartFraction 2 pi Over 3 EndFraction) + I sine (StartFraction 2 pi Over 3 EndFraction) ) and w = 6 (cosine (StartFraction pi Over 8 EndFraction) + I sine (StartFraction pi Over 8 EndFraction) ) , which geometric transformation of z on the complex plane describes the quotient StartFraction z Over w EndFraction ? Scale z by a factor of One-sixth, then rotate clockwise by StartFraction pi Over 8 EndFraction radians.
Scale z by a factor of 6, then rotate clockwise by StartFraction pi Over 8 EndFraction radians.
Scale z by a factor of One-sixth, then rotate counterclockwise by StartFraction pi Over 8 EndFraction radians.
Scale z by a factor of 6, then rotate counterclockwise by StartFraction pi Over 8 EndFraction radians.

A. Scale z by a factor of 1/6, then rotate clockwise by pi/8 radians.

Step-by-step explanation:

EDGE 2020

d

step-by-step explanation:

i used the pitagoras theoreme

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).