Sketch the graph of cosec , for .
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Sketch the graph of cosec , for .
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Solve the equation cot , for , giving your answers to three significant figures.
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Sketch the graph of sec , for .
Label any points of intersection with the coordinate axes and state the equations of any asymptotes.
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Starting with the identity
sin2 cos2
show that
cot2 cosec2
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Show that
sec2 sin tan sec
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Solve the equation cosec2 cosec for , giving your answers to one decimal place where appropriate.
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Show that
cot cosec sec cot2
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Solve the equation sec tan sec , for , giving your answers in exact form.
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Sketch the graph of sec , for .
Draw a suitable line on your graph to show that the equation sec has four solutions in the range .
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Use the definitions of the secant, cosecant and cotangent functions to show that
sec cot cosec .
Hence solve, in the range , the equation
sec cot
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Show that the equation
sec
can be rewritten in the form
Hence solve, in the range , the equation
sec
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Using the double angle formula sin sin cos , show that the equation
sec cosec cosec
can be rewritten in the form
cosec .
Hence solve, in the range , the equation
sec cosec cosec
giving your answers correct to 3 significant figures.
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Show that the equation
tan2 sec
can be rewritten in the form
Hence solve, in the range , the equation
tan2 sec
giving your answers correct to 3 significant figures.
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Rewrite tan cosec as a single trigonometric function.
Hence solve, in the range , the equation
tan cosec
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Solve, in the range , the equation
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Using the double angle formula sin sin cos , find the solutions to the equation
sec cosec cosec
in the range . Give your answers correct to 3 significant figures.
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Show that the equation
cot2 cosec
can be rewritten in the form
Hence solve, in the range , the equation
cot2 cosec
giving your answers correct to 3 significant figures.
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Sketch, in the interval , the graph of sec , include asymptotes and label the coordinates of all maximum and minimum points.
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Solve, in the range , the equation
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Solve, in the range , the equation
sec
Leaving your answers as exact values.
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Using the double angle formulae and , find the solutions to the equation
in the range . Give your answers correct to 3 significant figures.
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Solve, in the range , the equation
Leaving your answers as exact values.
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Sketch, in the interval , the graph of , include asymptotes and label the coordinates of all maximum and minimum points.
Deduce the maximum and minimum values of .
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