First, simply prefer finding the intersection of 2 lines, you have the right to set these equations equal to each other. So,
sin2θ = cos2θ
Now rather of trying to simplify and resolve, you might usage the unit circle.
You are watching: Find all points of intersection of the given curves
The just locations on the unit circle wbelow sine and also cosine have the same value is at π/4 and also 5π/4.
However before, they want you to discover ALL points of interarea so we need to come up with a basic equation to assist determine ALL points.
Due to the fact that π/4 and 5π/4 are π distance amethod from each various other (on the unit circle), we have the right to use this in our general equation. So,
2θ = π/4 + nπ wbelow n = 0,1,2,3,....
Now we deserve to simplify this to,
θ = π/8 * (4n+1) wbelow n = 0,1,2,3,....
This general formula dictates ALL points on which r2 = sin2θ and also r2 = cos2θ intersect.
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