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Solve graphically the cquation sin z c02n |
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Answer» Starting fromθ=0θ=0and going counterclockwise, the first time this is true is at 45 degrees, orπ4π4. It happens again at 225 degrees, or5π45π4, where they're both negative. The two have the samelengthat 135 degrees, but at that pointcos(θ)cos(θ)is negative andsin(θ)sin(θ)is positive, so the signs aren't equal. The same is true at 315 degrees -- they have the same length but the signs are opposite. You can keep going counterclockwise past 360 degrees and you hit the same lines again, but now the angles are 360+45 = 405 degrees (9π49π4) and 360+225 = 585 degrees (13π413π4). This continues on with more rotations -- the pattern is that every 180 degrees after 45 degrees, this solution occurs. So all solutions can be described with the expression: 45+180n45+180ndegreesorπ4+πnπ4+πnradianswherenncan be any integer. |
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