Trigonometry is Latin to You?
- Date: 2007-04-01 - Word Count: 513
Share This!
Not your cup of tea, huh? Try out the following steps:
1. Start with writing 1 identity on a piece of paper. An example would be Sin Square Theta+Cos Square Theta=1. Now, divide all the terms by Sin Square Theta. Do it your self and see the result. Neatly copy your working on a pocket size notebook. Write down today's date. This process will take up 15 minutes at the most.
2. Next time, divide all the terms by Cos Square Theta. Neatly jot down the working in your notebook and put down the date.
3. Do similar divisions of other identities.
4. If you do this once a day for just 3 weeks, you will understand which formula to use when a trigonometry problem stares at your face the next time around. If you still have problems, you can always ask your teacher in school or you can refer the problem to an online tutor. A reasonable good online math tutor should be able to help.
Now, Let us try solving a simple problem
A kite is flying at a height of 75 meters from the level ground, attached to a string inclined to an angle of 60 degree to the horizontal. Find the length of the string to the nearest meter.
Step1: to start with, first draw the required diagram according to the problem.
P
M O
Step2: Try relating the diagram with the given problem
Declare the necessary assumptions:
Let ‘ P' denote the position of the kite, and MP = 75 meters (the height of the kite)
And the string be held at the point O, The angle < MOP = 60 degree (given)
Therefore, OP is the length of the string
Step3: The next step is to apply the appropriate identities.
From the right angled triangle MOP,
OP = opposite leg of the acute angle < MOP
MP = hypotenuse
We will apply a basic trigonometric identity here
i.e., (opposite leg) / (hypotenuse ) = Sin < MOP
[As < MOP is the acute angle and the ratio Sine < MOP is the ratio between opposite leg to the hypotenuse.]
We have,
(OP) / (M P) = Sin < MOP
(OP) / (MP) = Sin 60 [< MOP = 60 (given)]
OP = (Sin 60) * (MP)
OP = (sin 60) * 75 [MP = 75 (given)]
OP = ((√ 3) / 2) * 75 [Sin 60 = ((√ 3) / 2) [value of Sin60 can easily be found out using trigonometric tables of standard angles]
O P = ((1.732) / 2) * 75 [(√ 3) = 1.732 (approx.)]
OP = 86 .6 [approx. ]
So, the length of the string is 86.6 meters (to the nearest meter)
For grasping a chapter thoroughly you must solve at least fifteen problems.
If you don't want to work that much, try solving the following problem:
A pole is being broken by the wind; the top struck the ground at an angle of 30 degree and at a distance of 8 m from the foot of the pole. Find the whole height of the pole.
Solve this problem and forget about solving 15 problems. You'd rather do something else!
Ishani Dutta is an educator who specializes in providing online tuition packages for Mathematics and English. For similar tips on different topics like pre-algebra, co-ordinate geometry, essay writing mailto:info@learningexpress.biz or mailto:learningexpress@getresponse.com or go to: http://www.learningexpress.biz for online help
1. Start with writing 1 identity on a piece of paper. An example would be Sin Square Theta+Cos Square Theta=1. Now, divide all the terms by Sin Square Theta. Do it your self and see the result. Neatly copy your working on a pocket size notebook. Write down today's date. This process will take up 15 minutes at the most.
2. Next time, divide all the terms by Cos Square Theta. Neatly jot down the working in your notebook and put down the date.
3. Do similar divisions of other identities.
4. If you do this once a day for just 3 weeks, you will understand which formula to use when a trigonometry problem stares at your face the next time around. If you still have problems, you can always ask your teacher in school or you can refer the problem to an online tutor. A reasonable good online math tutor should be able to help.
Now, Let us try solving a simple problem
A kite is flying at a height of 75 meters from the level ground, attached to a string inclined to an angle of 60 degree to the horizontal. Find the length of the string to the nearest meter.
Step1: to start with, first draw the required diagram according to the problem.
P
M O
Step2: Try relating the diagram with the given problem
Declare the necessary assumptions:
Let ‘ P' denote the position of the kite, and MP = 75 meters (the height of the kite)
And the string be held at the point O, The angle < MOP = 60 degree (given)
Therefore, OP is the length of the string
Step3: The next step is to apply the appropriate identities.
From the right angled triangle MOP,
OP = opposite leg of the acute angle < MOP
MP = hypotenuse
We will apply a basic trigonometric identity here
i.e., (opposite leg) / (hypotenuse ) = Sin < MOP
[As < MOP is the acute angle and the ratio Sine < MOP is the ratio between opposite leg to the hypotenuse.]
We have,
(OP) / (M P) = Sin < MOP
(OP) / (MP) = Sin 60 [< MOP = 60 (given)]
OP = (Sin 60) * (MP)
OP = (sin 60) * 75 [MP = 75 (given)]
OP = ((√ 3) / 2) * 75 [Sin 60 = ((√ 3) / 2) [value of Sin60 can easily be found out using trigonometric tables of standard angles]
O P = ((1.732) / 2) * 75 [(√ 3) = 1.732 (approx.)]
OP = 86 .6 [approx. ]
So, the length of the string is 86.6 meters (to the nearest meter)
For grasping a chapter thoroughly you must solve at least fifteen problems.
If you don't want to work that much, try solving the following problem:
A pole is being broken by the wind; the top struck the ground at an angle of 30 degree and at a distance of 8 m from the foot of the pole. Find the whole height of the pole.
Solve this problem and forget about solving 15 problems. You'd rather do something else!
Ishani Dutta is an educator who specializes in providing online tuition packages for Mathematics and English. For similar tips on different topics like pre-algebra, co-ordinate geometry, essay writing mailto:info@learningexpress.biz or mailto:learningexpress@getresponse.com or go to: http://www.learningexpress.biz for online help
Related Tags: teacher, online help, triangle, online tutor, online math tutor, trigonometry, pre-algebra
Your Article Search Directory : Find in Articles
Recent articles in this category:
- How Hypnotherapy Can be Used on Children
Today Hypnosis can be termed as a branch of medicine which is quite unique, whereas in the past this - Confidence Workshops For Children
Every parent wants their children to be confident, happy, highly motivated and enthusiastic in order - Inspiring Children Using NLP
Neuro-Linguistic Programming (NLP) is one of the most successful therapies in psychology today. Init - Writing Term Papers
Students often tend to put off a written assignment, considering it to be a chore too formidable to - Naming In Term Paper
Give a descriptive name to each of your concept in the paper. Adhere using terms like "our approach" - Introduction Section of a Research Paper
Your introductions should not exceed more than two pages (typed, double spaced). See again the examp - Getting a Feedback of Your Term Paper is Important!
Get the feedback of your work! Finish your paper, having written it well in advance, so that you hav - The 1950's - Was Life Better?
Iconic TV shows like I Love Lucy, Dennis the Menace and My Three Sons seem to indicate that the 1950 - Online Classroom Systems Makes Home Schooling Even More Attractive
In the past it went without saying that you would send your kids to public schools. With public scho - 8 Helpful Tips For Surviving Military Basic Training
Getting through military basic training takes a lot perseverance. During this training it is best to
Most viewed articles in this category:
- Culinary Cooking Schools and What They Teach
Culinary cooking schools prepare you for a job in the culinary industry by providing you with the kn - How To Learn Spanish Quickly Without Moving To Spain
Learning Spanish is a popular pastime, as well as a serious goal for many individuals. Whether it's - How To Improve Your Life With An Accredited Online College Degree
With the information super highway raring full steam ahead, quality accredited online college degree - Online Bachelor Degree Programs Go Mainstream
The Internet has seen an explosion in online bachelor degree programs in the last five to ten years - Online Degree Program Just A Click Away
You want to go shopping, but your car is low on gas. You want to know your account balance, but do n - Online Paralegal Degree Will Open Doors
An online paralegal degree may offer the possibility of improving your chances in the legal professi - What West Point Military School Looks For In A Candidate
West Point is looking for well rounded young men and women who are good students, good athletes, and - The Importance of Effective Accounting Programs
In the past, small businesses like mom and pop stores were not required to maintain any sort of acco - California Schools Educators Retirement System And Lionstone Group Create Investment Fund
The California State Teachers' Retirement System (CSTRS) is the second largest public pension fund i - A Taste of China - Seattle Schools New Guest Teacher Shares Language and Culture of Her Native Hom
The Seattle schools have a new "guest" teacher. Zhu Dan arrived in the Seattle schools in January