Trigonometry

1. Trigonometry what does logging have to do with trigonometry?

2. What is trigonometry and where did it originate? • Trig-o-nom-e-try n. • The study of relations between the side and angles of triangles. • “the first known table of chords was produced by the Greek mathematician Hipparchus in about 105 BC.”

3. Fun Facts  “The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus circa 150 BC, who compiled a trigonometric table using the sine for solving triangles. Ptolemy further developed trigonometric calculations circa 100 AD Development of trigonometry is not the work of any one man or nation. It first originated in India and the basic concepts of angle and measurements was noted in Vedic texts such as Srimad Bhagavatam. However, trigonometry in its present form was established in Surya Siddhanta and later by Aryabhata [5th century CE]. It should be noted that from the time of Hipparchus until modern times there was no such thing as a trigonometric ratio. Instead, the Indian civilization and after them the Greeks and the Muslims used trigonometric lines. Pythagoras of Samos (580? BC- 500? BC) was an Ionian Greek mathematician and also founder of the religious movement called Pythagoreanism. Nasir al-Din al-Tusi (1135-1213) (aka SharafeddinTusi) widely promulgated studies in trigonometry, which was compiled by him as a new subject in its own right for the first time. He also developed the subject of spherical trigonometry.” Read more: http://wiki.answers.com/Q/Who_are_the_mathematicians_that_developed_trigonometry#ixzz25YKGoDgt

4. When in life would we use trig? “Its used in science when the precise distances needs to be measured.” “The techniques in trigonometry are used for finding relevance in navigation particularly satellite systems and astronomy, naval and aviation industries, oceanography, land surveying, and in cartography (creation of maps). Now those are the scientific applications of the concepts in trigonometry, but most of the math we study would seem (on the surface) to have little real-life application. So is trigonometry really relevant in your day to day activities? You bet it is.” “Did you know that trigonometry is an arty science that can be used to measure the heights of mountains?Because this information is of great value for aircraft designing and navigation.

5. “Trigonometry finds a perfect partner in modern architecture. The beautifully curved surfaces in steel, stone and glass would be impossible if not for the immense potential of this science. So how does this work actually. In fact the flat panels and straight planes in the building are but at an angle to one another and the illusion is that of a curved surface.” www.mathworksheetscenter.com Functions: Sin=opposite/hypotenuse Cos=adjacent/hypotenuse Tan=opposite/adjacent

6. Given sin0=3/5, find sec0. a.3/5 b.4/5 c.5/3 b.5/4 Answer: sin0=3/5 sec0=5/4 5 3 4 2. Given csc0=13/5, find sec0xtan0 a.65/144 b.60/156 c.169/144 Answer:csc0=13/5=h/o Sec0xtan0=13/12 x 5/12=65/144 13 5 12 3.Given sec0=2, find csc0 x sin0 x cot0 a.2 b.1/ the square root of 2 c.1/ the square root of 3 Answer; sec0=2/1 csc0 x sin0 x cot0= 1/sin0 x sin0 x cort0=1/ the square root of 3

7. 1 Answer: • Choose: • 13/513/1212/55/12 • Which ratio represents cscA in the right triangle shown below?

8. In the right triangle shown below, OG = 7, DG = 8, and m<DOG = 90. What is the measure of <G to the nearest minute? • Choose: • 28º 95'28º 96'28º 57'28º 58' http://www.regentsprep.org/Regents/math/algtrig/ATT1/PracSpecial.htm I have seen this before but I don’t believe I've seen it like these questions.

9. How do logging companies use trig? • Logging companies use blue prints draw up to show the forest area in which they are going to harvest. They have to know at least 46 types of math in order to operate. They must know basic math/ algebra, first year algebra, geometry, second-year algebra/trigonmetry, and other topics. Some of the things they must know Coordinate Graphing 3D, Trigonometric/Circular Functions, and Graphs of Trigonometric Functions.

10. Graphs of trigonometric functions 

11. Coordinate Graphing 3D • A system of locating a point in space by its distance from the origin along three mutually perpendicular lines called the x-, y-, and z-axes. Looks interesting right?

12. Project of a later date!!! • Trigonometry cannon! There always seems to be interest in things that shoot. Here's how to do it with the new Trig functions.Use Space to shoot, Up/Down to control the barrel angle, Right/Left to roll the cannon around. The X key can be used to clear the cannonball paths.This is a cannon with the projectile motion calculated using the new Trig functions. The tip of the Barrel is also located using the Trig functions so that the Ball can be placed at the Barrel tip when it is fired.Wind is accounted for as a constant change to horizontal velocity. This is not a very realistic model, but it looks good enough for animation. In addition to changing the barrel angle and the wind, the trajectory can be further modified by changing the initial velocity or the acceleration due to gravity (Ay) in the scripts. http://scratch.mit.edu/projects/Paddle2See/77800

13. Unit circles!........... ……….Circles and triangles • The unit circle is just a circle with a radius of one. • How and why: the circles have triangles in them and that is how they are brought together and the math that consist of it see at www.mathisfun.com/gemometry/unit-circle.html • Circles and triangles are related.

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