Solve the equation sec for .
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Solve the equation sec for .
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Given that
tan
find the values of such that .
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Solve the equation
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Sketch the graphs of , where is measured in radians.
Label any points where the graphs intersect the coordinate axes.
Find the only solution to .
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Use the identity
to show that
can be written as
where to three significant figures.
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Show that the equation cosec2 cosec can be written as
Hence, or otherwise, solve the equation
cosec2 cosec
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Solve the equation
cos
State your answers as multiples of .
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Write down the domain and range for the function
Solve the equation
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Use a small angle approximation to estimate the solution to the equation
cot
Solve the equation cot .
Give your answer to three significant figures.
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Sketch the graph of sec for .
sec
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Solve the equation
cot2 cos cosec2
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Solve the equation cosec for .
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Given that
tan
find the values of such that .
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Solve the equation
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Use the identity
sincos sin sin cos
to show that
sin cos
can be written as
sin
Hence, or otherwise, solve the equation sin cos for .
Give your answers to three significant figures.
Write down the maximum value of sin cos and state the first positive value of for which it occurs. Give your value of to three significant figures.
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On the same axes, sketch the graphs of and , where is measured in radians.
Label any points where the graphs intersect the coordinate axes and each other.
Hence, or otherwise find the only solution to .
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Show that the equation tan2 sec can be written as
sec2 sec
Hence, or otherwise, solve the equation
tan2 sec
Give your answers to three significant figures.
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Solve the equation
cos cos
State your answers as multiples of .
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Write down the domain and range for the function
Solve the equation
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Use a small angle approximation to estimate the solution to the equation
cosec
Solve the equation cosec .
Give your answer to six decimal places.
Find the percentage error, to two significant figures, in the approximation from part (a) compared to your answer in part (b).
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Sketch the graph of for .
By adding three lines to your graph demonstrate how the equation
cot2
where is a constant has either 0, 4 or 8 real solutions.
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Solve the equation
cot2 sec2
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Solve the equation sec2 tan for .
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Given that
sin
and that
and
find the values of and .
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Solve the equation
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Find the value of ...
,
Briefly explain why .
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Show that cos sin can be written in the form cos, where and is an acute angle measured in radians.
Hence, or otherwise, solve the equation cos sin ,for
Give your answers to three significant figures.
Write down the minimum value of cos sin and the smallest positive value of for which it occurs. Give your value of to three significant figures.
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Solve the equation
cot2 cosec
giving your answers to three significant figures where appropriate.
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Solve the equation
cos4 cos
State your answers as multiples of .
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Write down the domain and range for the function
Solve the equation
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Use a small angle approximation to estimate the positive solution to the equation
sec
Give your answer to six decimal places.
Solve the equation sec .
Give your answer to six decimal places.
Find the percentage error, to two significant figures, in the approximation from part (a) compared to your answer in part (b).
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Determine the values of the constant for which the equation
cosec
has (i) no real solutions,
(ii) 1 real solution,
(iii) 2 real solutions,
(iv) 4 real solutions
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Solve the equation
cot2 cosec
Give your answers to one decimal place where appropriate.
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Solve the equation sin3 sin cos2 for .
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Given that
cos and tan
and that
find the possible values of and .
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Sketch the graph of for .
Label the point of intercept with the -axis and state the equations of any asymptotes.
Hence, or otherwise, write down the intercepts between the graph of
and
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Solve the equation sin cos ,for .
Give your answers to three significant figures.
Write down the maximum value of sin cos and the second positive value of for which it occurs. Give your value of θ to three significant figures.
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Solve the equation
sec4 tan2
giving your answers to three significant figures where appropriate.
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Solve the equation
cosec2
Give your answers to three significant figures.
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Write down the domain and range for the function
Solve the equation
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Use a small angle approximation to estimate the positive solution to the equation
cot cos
Give your answer to six decimal places.
Solve the equation cot cos .
Give your answer to six decimal places.
Find the percentage error, to two significant figures, in the approximation from part (a) compared to your answer in part (b).
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Solve the equation
sin4 cos
State your answers as multiples of .
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The number of real solutions to the equation
is determined by the value of the constant .
Find the number of real solutions for all values of , given that .
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Given that is a root of , solve the equation by factorisation.
Solve the equation
Give your answers to one decimal place where appropriate.
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