Trigonometry Final Product

GROUP MEMBERS:

Guan Zhou (Leader)

Chee Yong

Kai Yong

Vanessa

Pei Xuan 

All About Trigonometry

What is Trigonometry?

Trigonometry is the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. Now that you know what Trigonometry is, do you have any interest in Trigonometry?  

Pythagorean Theorem

It is called "Pythagoras' Theorem" and can be written in one short equation:

Note:

• c is the longest side of the triangle
• a and b are the other two sides

Life Applications on Astronomy

Life Applications on Astronomy

Astronomy – measurement of the positions and movements 

The biggest impact that trigonometry has had in Astronomy is in the finding of distances to nearby stars through the method of parallax.

Parallax

• When an object is viewed from two different positions it appears to move in relation to its background. This apparent movement is termed parallax. 

• In astronomy, parallax refers to the difference in direction of a celestial object when viewed by an observer from two widely separated points.
                                                                           

Trigonometric Parallax

Parallax can be used directly to determine the distance of nearby stars.

Life Applications on Architecture

Life Applications on Architecture

Uses:

• Calculate structural loads – used to calculate the right size a wall should be
• Calculate roof slopes – used to calculate the  angle a roof should be
• Find angles – used when putting together beams or trusses or complex architectural structures for buildings
• Chop down trees – used to know the height of the tree before cutting it down (also uses the *clinometer)

         *clinometer – an instrument used for measuring the angle or elevation of slopes.

Trigonometry Identities

Trigonometry Identities

• Finding the length of one or more sides of a shape
• Finding the angle at which different materials should be placed at.
• Finding the *sine of an angle will help when determining how much a certain material is needed to use in order to construct the building.
• Found in e.g. cars, benches and desks.

  *sine:The sine of an angle is defined in the context of a right triangle: for  the specified angle, it is the ratio of the length of the side that is opposite  that angle to (divided by) the length of the longest side of the triangle (i.e. the hypotenuse).

Conclusion

Conclusion

• We realised that trigonometry can be used in many areas such as astronomy and architecture they can aid in calculating many things they can also be used in cars desks and benches. Without really climbing a tree, you can find the height easily with trigonometry. They can be so widely used in real life applications and is very useful for most architects and astronomers.

• We can conclude that without trigonometry, life would be much more difficult. Without going through the troubles, you can easily find something so we think that it was a good invention by Archimedes and thanks to this many architects need not go through the trouble to calculate things, so it really helps in real life applications and not only in our tests and exams.

Bibliography

Bibliography

• http://www.oxforddictionaries.com/definition/english/trigonometry
• http://www.mathsisfun.com/pythagoras.html
•   “Excel HSC Physics” – Neville G. Warren Page 180
• “Architecture in Formation” – Andrew Saunders Page 225