MHB Where Do Polar Curves r=5sin(theta) and r=5cos(theta) Intersect?

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The polar curves r=5sin(theta) and r=5cos(theta) intersect at points where 5sin(theta) equals 5cos(theta). Dividing both sides by 5cos(theta) leads to the equation tan(theta) = 1. This results in solutions for theta at π/4 and 5π/4 within the specified range. Substituting these values back into either equation gives the corresponding r values of 5√2/2 for both intersections. Thus, the points of intersection are (5√2/2, π/4) and (5√2/2, 5π/4).
joshuapeterson
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Determine the polar coordinates of the two points at which the polar curves r=5sin(theta) and r=5cos(theta) intersect. Restrict your answers to r >= 0 and 0 <= theta < 2pi.
 
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Aren't you going to at least attempt it yourself? r= 5 sin(theta)= 5 cos(theta). What do you get if you divide both sides by 5 cos(theta)?
 

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