From: Subject: Trigonometry: sine, cosine, tangent Date: Tue, 28 Dec 2004 19:14:49 -0500 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0034_01C4ED11.803217D0" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 This is a multi-part message in MIME format. ------=_NextPart_000_0034_01C4ED11.803217D0 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.sec.org.za/maths/mtrigsin.html =EF=BB=BF Trigonometry: sine, cosine, tangent
Subject Area: Mathematics
Topic: Trigonometry
Grade: 10

Trigonometry: sine

Overnight something terrible has = happened:
All=20 the data on natural sine, cosine and tangent was completely wiped out = by one=20 of the worst computer bugs ever. On all computer screens the = mathematical=20 tables only show blank pages, scientific calculators don't react to = punching=20 in numbers, computer operators and IT-freaks (allegedly one of them = spread the=20 most efficient virus ever developed) work around the clock, Microsoft = Bill=20 Gates is fuming, scientists around the globe are extremely upset, some = assume=20 even infiltration from outer space.
But Soweto stays cool. Groups = of=20 learners have gathered at the SEC. They are surrounded by graph paper, = pencils, set squares, protractors, mathematical compasses, etc. They = are=20 putting their heads together to save the future of trigonometry. Can = the=20 situation be stabilized or is everything falling into bits and pieces? =
Find out, work it out.
Teams for the various trigonometric = ratios are=20 formed. You are a lucky member of the
sine team.
Give your all in saving the planet and = the=20 future of mathematics. Ask yourself: What does the sine ratio mean? =
It has=20 to do with right-angled triangles, it gives us the size of an angle, = if we=20 calculate the ratio of the length of the opposite side divided by the = length=20 of the hypotenuse. But we can no longer look for this ratio in the=20 mathematical table or use a scientific calculator and find the size of = the=20 angle. How is it possible to find at least an approximation of these = values=20 and get the whole thing started again?
Quite simple: equip = yourself with=20 the geometrical requirements and stationary and go for a trigonometric = workout.=20

Instructions:
1. draw a circle of radius 10cm into a = co-ordinate=20 system, with the centre of the circle at the origin.
2. construct = an angle=20 of, for instance, 400 through the origin and with the = positive=20 x-axis. This angle will intersect the circle. From this intersection = point=20 draw a perpendicular line to the x-axis. Now you have constructed a=20 right-angled triangle with one angle of 400.
3. measure = the=20 length of the side opposite the angle of 400, divide this = length by=20 10cm (the hypotenuse is in this case always the radius of the circle) = and=20
4. that gives you an approximate value for the sine of = 400.=20

Applying the same method it is very easy now to find the = approximate=20 sine values for the angle of 100, 200, = 300,=20 500, 600, 700 and 800.=20

3Dsec2001=20

Record your sine values in the table below:=20

sin 100 sin 200 sin 300 sin 400 sin 500 sin 600 sin 700 sin 800
               

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=C2=A9Science Education Centre,=20 2001
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