Help in A level maths needed!
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Help in A level maths needed!

[From: ] [author: ] [Date: 11-05-04] [Hit: ]
...-sin( pi/4) is the y-polar coordinate sqrt(2)/2.Multiply top and bottom by sqrt(2)/ sqrt(2) (by 1) to cancel out the top sqrt to get this answer.-you have to use the unit circle.......
Anyone know how to change Sin(Pi/4) into a fraction?
The answer is 1/Square root 2 but I don't know how to get that....

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sin( pi/4) is the y-polar coordinate sqrt(2)/2. Multiply top and bottom by sqrt(2)/ sqrt(2) (by "1") to cancel out the top sqrt to get this answer.

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you have to use the unit circle. on the unit circle, for pi/4, the x and y coordinates refer to the cos and sin coordinates, respectively. And the y coordinate of pi/4 is (square root 2)/2 which simplifies to 1/square root 2.

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2 pi radians is 360 degrees.
pi/4 is 45 degrees
Therefore, if you go 1 unit east and 1 unit north, the resulting radius is sqrt2.
sin of an angle is the north leg divided by the radius.
sin(pi/4) = 1(/sqrt 2)
..

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Pi/4 to me is 45 degrees. Draw a 45 degree triangle and label the sides. From your textbook a 45 degree right angle triangle has sides 1-1-root(2). Where root(2) is the hypothenuse. Sine of one of the 45 degrees angles is the opposite side divided by the hypothenuse or 1/root(2).

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Pi / 4 = 45 degrees

Imagine that you have a right angled triangle with shorter sides both of length 1. This will also be an isoceles, so there will be a 90 degrees and two 45 degree angles.

By pythagoras:

root(1^2 + 1^2) = root 2 = hypotenuse

sin 45 = opposite / hypotenuse
sin 45 = 1 / root 2
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