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| Circular Functions |
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| Statement: |
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| If 'n' be any integer then, |
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| i) sin (2pn + q) = sin q |
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| ii) cos (2pn + q) = cos q |
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| Proof: |
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| Draw a unit circle with centre 'O'. |
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| Let XOX' and YOY' be the coordinate axes. |
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| Let a variable point A on the circumference of the circle move from the position A (1,0) to the final position P(q) along the circumference of the circle. |
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| Let AP be the arc, so that arc AP subtends angle q at the centre. Let us suppose that the variable point A makes n complete rotations and further moves through arc length q. Then finally it comes to the position P. |
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| Then arc length covered by the variable point along the circumference is (2np + q). |
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 |
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| = abscissa of the P(q) |
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=  |
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| = ordinate of the P(q) |
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| = sin q |
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| Note: |
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