What value(s) of ϑ, in radians make(s) x minimum?

He relationship between rectangular and rotational coordinates can be represented by the vector equation: r = xi +yj = rcos(theta)i+rsin(theta)j What values in radians makes x minimum y maximum and x = -y Ans : x minimum = -r when theta = 180 degrees + any multiple of 360 degrees y minimum = -r when theta = 270 degrees + any multiple of 360 degrees x = -y when theta = 135 degrees + any multiple of 180 degrees.

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough