Sine, cosine, tangent

There are 60 NRICH Mathematical resources connected to Sine, cosine, tangent
Cosines Rule
problem
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Cosines rule

Age
14 to 16
Challenge level
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Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.
Three by One
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Three by one

Age
16 to 18
Challenge level
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There are many different methods to solve this geometrical problem - how many can you find?
Where is the dot?
problem
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Where is the dot?

Age
14 to 16
Challenge level
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A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
Three cubes
problem
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Three cubes

Age
14 to 16
Challenge level
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Can you work out the dimensions of the three cubes?
Belt
problem
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Belt

Age
16 to 18
Challenge level
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A belt of thin wire, length L, binds together two cylindrical welding rods, whose radii are R and r, by passing all the way around them both. Find L in terms of R and r.
Inscribed in a Circle
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Inscribed in a circle

Age
14 to 16
Challenge level
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The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?
Sine and Cosine
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Sine and cosine

Age
14 to 16
Challenge level
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The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?
Doesn't add up
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Doesn't add up

Age
14 to 16
Challenge level
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In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Far Horizon
problem
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Far horizon

Age
14 to 16
Challenge level
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An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
LOGOSquares
problem
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LOGOsquares

Age
16 to 18
Challenge level
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Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.