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Exploring Trigonometry Identities

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on 22 February 2016

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Transcript of Exploring Trigonometry Identities

Ancient mathematics and modern methods
Trigonometry comes from the greek words "trigonon" meaning triangle and "metria" meaning measure.

Egyptians planned the construction of the pyramids through the knowledge of the properties of similar triangles, which led to the development of trigonometric ratios in right angled triangles.
Later on cartography and navigation in the early 15th century were said to have flourished because of trigonometry and methods of triangulation.
We certainly no longer need trigonometry for map making and navigation, because in the 21st century a click of a button does it all for us.
But the satellites orbiting the earth to create the accurate maps we have to day, are all carefully positioned using trigonometrical calculations.
Exploring Trigonometry Identities
Questions
Find the exact value of Sin(75) without using your GDC

Prove this identity: (sinA + cosA)(sinB+CosB)= Sin(A+B)+ Cos (A-B)

Express 4-2cos A in terms of cos2A
Pythogorian identities
using the unit circle to prove the Pythagorean identity
Use the unit circle
to prove the tangent identity
Graphs and Co-function identities
sin(X)=cos(90-x)
cos(X)=sin(90-x)
Sin Graph
Cos graph
Compound/Double and half Angles
Tan Graph
Proving compound angles identities
Proving double angle identities
Use the double angle identities to
find the half angle identities
2
by;
Malek Sma
Full transcript