Work out the length of the missing side in the following right-angled triangle.
Using your answer from part (a) to help, write down the values of the following:
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Work out the length of the missing side in the following right-angled triangle.
Using your answer from part (a) to help, write down the values of the following:
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Show that
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Solve the equation
,
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Solve the equation .
Hence, or otherwise, solve the equation for .
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Solve the equation for , giving your answers to one decimal place.
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Sketch the graph of for .
Solve the equation for .
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Solve the equation for .
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Solve the equation for .
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Solve the equation 2 sin for .
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Show that the equation sin2 cos can be written in the form cos2 cos , where , and are integers to be found.
Hence, or otherwise, solve the equation sin2 cos for .
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Given that find the possible values of and .
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Solve the equation sin for .
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Solve the equation sin cos cos for .
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A right-angled triangle has hypotenuse 8 cm. One of its other sides is 5 cm.
Find exact values for , and , where is the smallest angle in the triangle.
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Show that .
Hence, or otherwise, solve the equation tan3 tan2 tan for , giving your answers to 1 decimal place where appropriate.
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A seagull sits on the surface of the sea and moves up and down as waves pass.
Its height, metres, above its position in calm water is modelled by the function sin where is the time in seconds after timing commences.
Sketch a graph of against for showing the coordinates of the points of intersection with the axis.
How many times in the first minute after timing commences is the seagull 0.25 metres above its calm water position?
Find the time at which the seagull is first 0.25m above its calm water position and moving downwards. Give your answer to 3 significant figures.
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Solve the equation sin cos for , giving your answers to 1 decimal place.
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Solve the equation sin2 cos for
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Given that the angle is obtuse and that sin , find the exact value of cos .
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Solve the equation tan for .
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Solve the equation tan sin for .
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An isosceles triangle has sides 8 cm, 8 cm and 4 cm and equal base angles .
Find exact values for sin ,cos and tan .
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Show that satisfies the equation .
Hence solve the equation cos3 cos2 cos for .
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A seagull sits on the surface of the sea and moves up and down as waves pass.
Its height, metres, above its position in calm water is modelled by the function sin where is the time in seconds after timing commenced.
Find the first time the seagull is 0.3 metres above its calm water position.
Give your answer to 2 decimal places.
How many times in the first minute after timing commences is the seagull 0.3 metres above its calm water position?
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Solve the equation sin cos for , giving your answers to 1 decimal place.
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Solve the equation cos2 sin for , giving your answers to 1 decimal place where appropriate.
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Given that the angle is reflex and that cos , find the exact value of tan .
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Solve the equation sin2 for .
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Solve the equation sintan for , giving your answers to 1 decimal place where appropriate.
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For the triangle in the diagram find exact values for sin ,cos and tan .
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Find all the values of in the range which satisfy the equation tan3 tan2 tan , giving your answers to 1 decimal place.
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A seagull sits on the surface of the sea and moves up and down as waves pass.
Its height, metres, above its position in calm water is modelled by the function where is the time in seconds after timing commences.
Find the amount of time the seagull is more than 0.5 metres above its calm water position in the first 20 seconds after timing commences.
Give your answer correct to 3 significant figures.
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