PLEASE REPLY TO EACH DISCUSSION WITH SIGNIFICANT CONTENT. THERE ARE TWO DISCUSSIONS. DO NOT JUST AGREE WITH THE STUDENT BUT PROVIDE SUPPORTING CONTENT IF YOU AGREE OR DISAGREE. THERE ARE TWO DISCUSSION RESPONSE. PLEASE RESPOND WITH A MINUMUM OF 100 words FOR EACH DISCUSSION.
1. Explain why trigonometric functions are periodic.
2. In A trigonometry function is common for more than one angle to have the same value for the sine or cosine, or other function. The occurrence of this is a result of a trigonometry functions being periodic. A periodic function is a function whose output values repeat at regular intervals. In form a periodic function is f(x)=f(x+k) for a constant k,. The constant k is the period and the interval that the function has a non repeating pattern before it repeats itself over again. The trigonometry function repeats after the fixed interval given in the function. This is sometimes also called a circular function because it goes around and around.
1. Give an example of application of trigonometry to real life problems.
2. There are so many different uses for trigonometry, the discipline itself deals with ratios, angles , and sides as they relate to each other in a given circumstance. Trigonometry can be used to measure unknown heights using measurements other than the immeasurable height. An example of this would be finding a buildings height or a mountains height. It can also be used to measure distances. Navigational uses include oceanic travel distance to shore, or the height of the tide. For larger scale distances trigonometry can be used to tell the distance the moon is from the sun at any given time. In a more abstract sense, trigonometry can be used to study light and soundwaves that can be graphed. Architects use ratios and other functions of trigonometry to calculate things like slope, shade, light angles, and structural loads that a building can handle.
I also wanted to add that every sport ever includes trig, but most atheltes are not using it to problem solve like they could be.
Week 3 Discussion
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1. Trigonometric functions are periodic because a periodic function is a function whose outputs repeat in regular intervals. An important trig periodic function are functions which repeat over intervals of 2 radians. Trigonometric functions repeat themselves since they are used in the interpretation of circles. The most unique periodic functions are sine and cosine. A good example is when you can cut and paste parts of the graph horizontally.
2. A couple of examples of real life uses of trigonometry are; measuring the height of a building or a mountain, uses in navigation, aviation, criminology. The use in criminology is at a crime scene to determine the trajectory of a projectile or to estimate the cause of a collision in a car accident. In aviation, its is used to determine the effects of how wind plays a role in the flight. In navigation, trigonometric functions and a compass help pinpoint a location and also find the distance.
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