Selected: Edexcel A Level Maths - Pure Maths
AS & A2 (Whole Course) - All Questions - Casio fx-991EX
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AS & A2 (Whole Course) - All Questions - Casio fx-991EX
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Polar Curves
Polar Areas
Polar Coordinates - Graph sketching - Circle: r = a
Investigate polar curves with equations of the form: $r = a$ for various values of the constant $a$.
Polar Coordinates - Graph sketching - r = a trig(bt)
Investigate polar curves with equations of forms like \(r = a \cos \left( {b\theta } \right)\) and \(r = a \sin \left( {b\theta } \right)\)
for various trigonometric functions and various values of the constants \(a\) and \(b\).
With \(a = 1\) and \(b = 1\),
polar curves of forms like \(r = \cos \left( {\theta } \right)\) can be investigated.
With \(a = 1\),
polar curves of forms like \(r = \cos \left( {b\theta } \right)\) can be investigated.
With \(b = 1\),
polar curves of forms like \(r = a \cos \left( {\theta } \right)\) can be investigated.
Pay close attention to the number of loops.
for various trigonometric functions and various values of the constants \(a\) and \(b\).
With \(a = 1\) and \(b = 1\),
polar curves of forms like \(r = \cos \left( {\theta } \right)\) can be investigated.
With \(a = 1\),
polar curves of forms like \(r = \cos \left( {b\theta } \right)\) can be investigated.
With \(b = 1\),
polar curves of forms like \(r = a \cos \left( {\theta } \right)\) can be investigated.
Pay close attention to the number of loops.
Polar Coordinates - Graph sketching - Investigate Polar Spirals
Investigate polar spirals with various equations. Experiment with different ranges of the angle θ.
Polar Coordinates - Graph sketching - r = a(p + q trig(t))
Investigate polar curves with equations like \(r = a \left( {p + q \cos \left( \theta \right)} \right)\)
for various trigonometric functions and various values of the constants \(a\), \(p\) and \(q\).
Pay close attention to any loops or symmetry or occurences of cusps.
With \(a = 1\), \(p = 1\) and \(q = 1\),
polar curves of forms like \(r = 1 + \cos \left( \theta \right)\) can be investigated.
With \(a = 1\) and \(p = 1\),
polar curves of forms like \(r = 1 + q \cos \left( \theta \right)\) can be investigated.
With \(p = 1\),
polar curves of forms like \(r = a \left( {1 + q \cos \left( \theta \right)} \right)\) can be investigated.
With \(a = 1\),
polar curves of forms like \(r = p + q \cos \left( \theta \right)\) can be investigated.
for various trigonometric functions and various values of the constants \(a\), \(p\) and \(q\).
Pay close attention to any loops or symmetry or occurences of cusps.
With \(a = 1\), \(p = 1\) and \(q = 1\),
polar curves of forms like \(r = 1 + \cos \left( \theta \right)\) can be investigated.
With \(a = 1\) and \(p = 1\),
polar curves of forms like \(r = 1 + q \cos \left( \theta \right)\) can be investigated.
With \(p = 1\),
polar curves of forms like \(r = a \left( {1 + q \cos \left( \theta \right)} \right)\) can be investigated.
With \(a = 1\),
polar curves of forms like \(r = p + q \cos \left( \theta \right)\) can be investigated.
Polar Coordinates - r = p trig(q - t)
Investigate polar curves with equations like \(r = p \sec \left( q - \theta \right)\)
for various trigonometric functions and various values of the constants \(p\) and \(q\).
Pay close attention to any loops or symmetry or occurences of cusps.
for various trigonometric functions and various values of the constants \(p\) and \(q\).
Pay close attention to any loops or symmetry or occurences of cusps.
Polar Coordinates - r = a trig²(t)
Investigate polar curves with equations of forms like \(r = a{\cos ^2}\left( \theta \right)\)
for various trigonometric functions and various values of the constant \(a\).
Pay close attention to any loops or symmetry or occurences of cusps.
for various trigonometric functions and various values of the constant \(a\).
Pay close attention to any loops or symmetry or occurences of cusps.
Polar Coordinates - r² = a trig(bt)
Investigate polar curves with equations of forms like \({r^2} = a \cos \left( {b\theta } \right)\)
for various trigonometric functions and various values of the constants \(a\) and \(b\).
With \(a = 1\) and \(b = 1\),
polar curves of forms like \({r^2} = \cos \left( {\theta } \right)\) can be investigated.
With \(a = 1\),
polar curves of forms like \({r^2} = \cos \left( {b\theta } \right)\) can be investigated.
With \(b = 1\),
polar curves of forms like \({r^2} = a \cos \left( {\theta } \right)\) can be investigated.
Pay close attention to any loops or symmetry or occurences of cusps.
for various trigonometric functions and various values of the constants \(a\) and \(b\).
With \(a = 1\) and \(b = 1\),
polar curves of forms like \({r^2} = \cos \left( {\theta } \right)\) can be investigated.
With \(a = 1\),
polar curves of forms like \({r^2} = \cos \left( {b\theta } \right)\) can be investigated.
With \(b = 1\),
polar curves of forms like \({r^2} = a \cos \left( {\theta } \right)\) can be investigated.
Pay close attention to any loops or symmetry or occurences of cusps.