Vector A has x and y components of equal magnitude. Find possibledirections for

Question

Vector A has x and y components of equal magnitude. Find possibledirections for vector A? In what way do I go about finding the possible directions? I have the answer as 45, 135, 225, and 315 degrees but don't know how these answers where brought about. I get that if both vector component magnitudes are equal and you use the inverse trig function to find the direction it always comes out to 45 degrees. I see a patter of 90 degree differences. I need a pictorial answer and example. Lastly, if the vectors have the same magnitude how can an answer other than 45 degrees be arrived at. Do use explicit calculations!

Explanation / Answer

X = Acos theta

Y = A sin theta

X = Y

Acos theta = A sin theta

cos theta = sin theta

45 degree

tan theta = Y/X

if both Y and X are positive than 1st quadrant = 45 degree anticlock wise from +x axis

if X is negative and Y is positive

2nd quadrant = 135 degree anti clock wise from +x axis

if both X and Y are negative

3rd quadrant = 225 degree anticlock wise from +x axis

if X is positive and Y is negative

4th quadrant = 315 degree  anticlock wise from +x axis

if

Related Questions

Navigate

• Browse (All)
• Browse V
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.