Why is it important to know the sum/difference & Double/Half angle identities? Also, if you use a citation it needs to be different for each person. Too many people are copying answers from people and posting them.
HEY IT IS TAYLOR HERE AND HERE IS MY COMMENT ON THIS WEEKS BLOG!!!
It is important to know the Double/Half angle identities because of how we need them in trig. We need ‘their formulas so that we can find any and all of the unknown trig. Functions’ (http://www.freemathhelp.com/trig-double-angles.html). By knowing these formulas you can automatically determine certain aspects of trig.. ‘Like if you know what Sin 15 is then you would use these formulas to find that Sin 30 equals ½’ (http://www.freemathhelp.com/trig-double-angles.html).
It is important to know the sum/difference angle identities because of what they are used for. For instance the addition (and subtraction) problems are used to ‘find the exact values of trigonometric expressions and simplifying expressions to obtain the identities’ (from the Advanced Mathematics by Richard G. Brown.) We can also use their formulas so that we can verify some identities that you may have already seen.
These process help find, simplify, and find the exact values of certain aspects of an equation for an angle so with these reasons and the reasons above we truly do need Double/Half angle identities and sum/difference angle identities.
I still do not know how to site so… the Advanced Mathematics by Richard G. Brown http://www.freemathhelp.com/trig-double-angles.html http://www.freemathhelp.com/trig-double-angles.html (and I believe that is it ,… I did my best so until tomorrow Ja Ne!!)
this is lawrence. i got all my information online, so nobody else take it!
In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles. These are distinct from triangle identities, which are identities involving both angles and side lengths of a triangle. Only the former are covered in this article.These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
The fact that the triple-angle formula for sine and cosine only involves powers of a single function allows one to relate the geometric problem of a compass and straightedge construction of angle trisection to the algebraic problem of solving a cubic equation, which allows one to prove that this is in general impossible, by field theory.
It is important to know the Double/Half angle identities because of how we need them in trig. We need ‘their formulas so that we can find any and all of the unknown trig.
An identity is an equality relationship between two mathematical expressions.In the sum and difference identities alpha and beta denotes the measure of the difference of the two angles alpha and beta. Oncethis identity is established it can be used to easily derive other important identities.The verification of this formula is somewhat complicated. Perhaps the most diffcult part of the proof is the complexity of the notation.
The half and difference identities equate trigonometric functions of half-angles to expressions that involve only trigonometric functions of single angles.If an angle in question is a variable, these formulas are sometimes the only means by which the trigonometric expression can be simplified. Even when an angle is known, these identities can be useful in simplifying expressions. They should be memorized.
Citiations
Price, Thomas E. "TRIGONOMETRIC IDENTITIES." The University of Arkon, 17 Aug. 2001. Web. 20 Oct. 2010. .
SparkNotes Editors. “SparkNote on More Trigonometric Identities.” SparkNotes.com. SparkNotes LLC. n.d.. Web. 20 Oct. 2010.http://www.sparknotes.com/math/trigonometry/moreidentities/section1.rhtml
This is Nathan with a respons to the Week 8 Blog Prompt.
The sum/difference identities are the formulas we learned from chapter 10 section 1. That's the sine and cosine, and also the tangent from section 2. These formulas are very important because they help us find the exact value of an angle that is not in the trig chart. They do this by finding two angles from the trig chart that add or subtract that give you the angle you are looking for, and you just plug them into the formula, and get your answer. The double-angle formulas are the ones we learned today with sine, cosine, and tangent. The half-angle formulas are all of the ones with the square root. These are important because they are used whenever expressions involving trigonometric functions need to be simplified. You try to avoid having to use the formulas with the square roots in them, unless you absolutely have to use it. Again, trig is just a bunch of formulas that need to be memorized.
"In mathematics, trigonometric identities (or trig identities for short) are equations involving trigonometric functions that are true for all values of the occurring variables. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common trick involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity."
"In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles. These are distinct from triangle identities, which are identities involving both angles and side lengths of a triangle. Only the former are covered in this article.
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity."
These are equations involving trigonometric functions that are true for all values of the occurring variables. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common trick involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
It is important for us to know the sum/difference and double/half angle because the identities shows that the cosine of the difference of two angles is related to the cosines and sines of the angles themselves. The identities are very useful whenever you are simplifying expressions that involves trigonometric functions.
It is important to know these because they are used quite frequently. "This problem reduces to just simple substitutions." - http://math.ucsd.edu/~wgarner/math4c/textbook/chapter6/doublehalfangles.htm
The problems for double angles and half angles mostly do simplify to substitutions.
Sum and difference identities are important to know because they allow you to find the alpha and/or beta pretty easy.
The sum and difference identities are the things we learned in 10-1 & 10-2. They are helpful because they help us find exact values of angles that are not found on the trig chart on on the unit circle. The double/half angle identities are the ones we learned today. the half angle ones included the square roots. It is very simple to solve all of these problems with the identities. It just includes a lot of memorization and application.
The trig. identities are important identities that involve sums or differences of angles. An identity that shows that the cosine of the difference of two angles is related to the cosines and sines of the angles themselves. Identities involving sin 2x of cos 2x are called double-angle identities. These identities are derived using the sum and difference identities. http://library.thinkquest.org/20991/alg2/trigi.html
Double and Half angle identities are important because they help find the theta equal to the theta divided by two formulas. Thus, giving us the answer to certain trigonometry formulas that would usually be unsolvable with the usual identities. “One reason these formulas are of special interest is that they allow us to compute values of trigonometric functions for arbitrarily small arguments, simply by applying them as many times as desired. It was through the clever use of half-angle formulas, for instance, that the well-renowned Greek mathematician Archimedes was able to compute the value of π to three decimal places, an amazing feat for his day.” Also, combining two Double and Half Angle Identities could combine to make tangent and co-tangent to come up with a way to solve trigonometric functions of decimals such as Archimedes’ great pi discovery.
http : / / www . math amazement . com / Lessons / Pre – Calculus / 05 _ Analytic – Trigonometry / double – angle – and – half – angle – formulas .html
The trig. identities are important identities that involve sums or differences of angles. An identity that shows that the cosine of the difference of two angles is related to the cosines and sines of the angles themselves. This identity is given below (A and B are used in place of alpha and beta, respectively since HTML does not support Greek characters).
cos (A - B) = (cos A)(cos B) + (sin A)(sin B)
The figure below gives a graphical representation of the cosine identity.
This identity is useful when you are asked to find the cosine of a non-30o-45o-60o-90o angle, such as 10o. Example:
1. Problem: Find cos 15o.
Solution: Write 15o in terms of angles with known trig. ratio values.
cos (45o - 30o)
Use the cosine identity to rewrite the expression.
(cos 45o)cos 30o + (sin 45o)sin 30o
Using the values you know for the trig. ratios of special angles, rewrite the expression.
HEY IT IS TAYLOR HERE AND HERE IS MY COMMENT ON THIS WEEKS BLOG!!!
ReplyDeleteIt is important to know the Double/Half angle identities because of how we need them in trig. We need ‘their formulas so that we can find any and all of the unknown trig. Functions’ (http://www.freemathhelp.com/trig-double-angles.html). By knowing these formulas you can automatically determine certain aspects of trig.. ‘Like if you know what Sin 15 is then you would use these formulas to find that Sin 30 equals ½’ (http://www.freemathhelp.com/trig-double-angles.html).
It is important to know the sum/difference angle identities because of what they are used for. For instance the addition (and subtraction) problems are used to ‘find the exact values of trigonometric expressions and simplifying expressions to obtain the identities’ (from the Advanced Mathematics by Richard G. Brown.) We can also use their formulas so that we can verify some identities that you may have already seen.
These process help find, simplify, and find the exact values of certain aspects of an equation for an angle so with these reasons and the reasons above we truly do need Double/Half angle identities and sum/difference angle identities.
I still do not know how to site so…
the Advanced Mathematics by Richard G. Brown
http://www.freemathhelp.com/trig-double-angles.html
http://www.freemathhelp.com/trig-double-angles.html
(and I believe that is it ,… I did my best so until tomorrow Ja Ne!!)
this is lawrence. i got all my information online, so nobody else take it!
ReplyDeleteIn mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles. These are distinct from triangle identities, which are identities involving both angles and side lengths of a triangle. Only the former are covered in this article.These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
The fact that the triple-angle formula for sine and cosine only involves powers of a single function allows one to relate the geometric problem of a compass and straightedge construction of angle trisection to the algebraic problem of solving a cubic equation, which allows one to prove that this is in general impossible, by field theory.
http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Double-.2C_triple-.2C_and_half-angle_formulae
i forgot how to cite, but i got all that information from that website.
It is important to know the Double/Half angle identities because of how we need them in trig. We need ‘their formulas so that we can find any and all of the unknown trig.
ReplyDeleteAn identity is an equality relationship between two mathematical expressions.In the sum and difference identities alpha and beta denotes the measure of the difference of the two angles alpha and beta. Oncethis identity is established it can be used to easily derive other important identities.The verification of this formula is somewhat complicated. Perhaps the most diffcult part of the proof is the complexity of the notation.
ReplyDeleteThe half and difference identities equate trigonometric functions of half-angles to expressions that involve only trigonometric functions of single angles.If an angle in question is a variable, these formulas are sometimes the only means by which the trigonometric expression can be simplified. Even when an angle is known, these identities can be useful in simplifying expressions. They should be memorized.
Citiations
Price, Thomas E. "TRIGONOMETRIC IDENTITIES." The University of Arkon, 17 Aug. 2001. Web. 20 Oct. 2010. .
SparkNotes Editors. “SparkNote on More Trigonometric Identities.” SparkNotes.com. SparkNotes LLC. n.d.. Web. 20 Oct. 2010.http://www.sparknotes.com/math/trigonometry/moreidentities/section1.rhtml
This is Nathan with a respons to the Week 8 Blog Prompt.
ReplyDeleteThe sum/difference identities are the formulas we learned from chapter 10 section 1. That's the sine and cosine, and also the tangent from section 2. These formulas are very important because they help us find the exact value of an angle that is not in the trig chart. They do this by finding two angles from the trig chart that add or subtract that give you the angle you are looking for, and you just plug them into the formula, and get your answer.
The double-angle formulas are the ones we learned today with sine, cosine, and tangent. The half-angle formulas are all of the ones with the square root. These are important because they are used whenever expressions involving trigonometric functions need to be simplified. You try to avoid having to use the formulas with the square roots in them, unless you absolutely have to use it.
Again, trig is just a bunch of formulas that need to be memorized.
Cite:http://en.wikipedia.org/wiki/Angle_sum_and_difference_identities#Double-.2C_triple-.2C_and_half-angle_formulae
"In mathematics, trigonometric identities (or trig identities for short) are equations involving trigonometric functions that are true for all values of the occurring variables. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common trick involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity."
ReplyDeleteCite:
http://www.wordiq.com/definition/Trigonometric_identities
hey guyz its feroz doin my blog k
ReplyDelete"In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles. These are distinct from triangle identities, which are identities involving both angles and side lengths of a triangle. Only the former are covered in this article.
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity."
http://en.wikipedia.org/wiki/List_of_trigonometric_identities
These are equations involving trigonometric functions that are true for all values of the occurring variables. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common trick involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
ReplyDeleteCitation: http://fact-archive.com/encyclopedia/Trigonometric_identity
This comment has been removed by the author.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteIt is important for us to know the sum/difference and double/half angle because the identities shows that the cosine of the difference of two angles is related to the cosines and sines of the angles themselves. The identities are very useful whenever you are simplifying expressions that involves trigonometric functions.
ReplyDeleteCitations:
http://www.wordiq.com/definition/Trigonometric_identities
http://library.thinkquest.org/20991/alg2/trigi.html
it's dylan.
ReplyDeleteIt is important to know these because they are used quite frequently.
"This problem reduces to just simple substitutions." - http://math.ucsd.edu/~wgarner/math4c/textbook/chapter6/doublehalfangles.htm
The problems for double angles and half angles mostly do simplify to substitutions.
Sum and difference identities are important to know because they allow you to find the alpha and/or beta pretty easy.
IDK actually... :/
The sum and difference identities are the things we learned in 10-1 & 10-2. They are helpful because they help us find exact values of angles that are not found on the trig chart on on the unit circle. The double/half angle identities are the ones we learned today. the half angle ones included the square roots. It is very simple to solve all of these problems with the identities. It just includes a lot of memorization and application.
ReplyDeleteThe trig. identities are important identities that involve sums or differences of angles. An identity that shows that the cosine of the difference of two angles is related to the cosines and sines of the angles themselves. Identities involving sin 2x of cos 2x are called double-angle identities. These identities are derived using the sum and difference identities. http://library.thinkquest.org/20991/alg2/trigi.html
ReplyDeleteDouble and Half angle identities are important because they help find the theta equal to the theta divided by two formulas. Thus, giving us the answer to certain trigonometry formulas that would usually be unsolvable with the usual identities.
ReplyDelete“One reason these formulas are of special interest is that they allow us to compute values of trigonometric functions for arbitrarily small arguments, simply by applying them as many times as desired. It was through the clever use of half-angle formulas, for instance, that the well-renowned Greek mathematician Archimedes was able to compute the value of π to three decimal places, an amazing feat for his day.”
Also, combining two Double and Half Angle Identities could combine to make tangent and co-tangent to come up with a way to solve trigonometric functions of decimals such as Archimedes’ great pi discovery.
http : / / www . math amazement . com / Lessons / Pre – Calculus / 05 _ Analytic – Trigonometry / double – angle – and – half – angle – formulas .html
The trig. identities are important identities that involve sums or differences of angles. An identity that shows that the cosine of the difference of two angles is related to the cosines and sines of the angles themselves. This identity is given below (A and B are used in place of alpha and beta, respectively since HTML does not support Greek characters).
ReplyDeletecos (A - B) = (cos A)(cos B) + (sin A)(sin B)
The figure below gives a graphical representation of the cosine identity.
This identity is useful when you are asked to find the cosine of a non-30o-45o-60o-90o angle, such as 10o. Example:
1. Problem: Find cos 15o.
Solution: Write 15o in terms of
angles with known trig. ratio values.
cos (45o - 30o)
Use the cosine identity to
rewrite the expression.
(cos 45o)cos 30o + (sin 45o)sin 30o
Using the values you know for the trig.
ratios of special angles, rewrite the
expression.
SQRT(2) SQRT(3) SQRT(2) 1
------- * ------- + ------- * -
2 2 2 2
Perform the indicated multiplications.
SQRT(6) SQRT(2)
------- + -------
4 4
SQRT(6) + SQRT(2)
-----------------
4
There is also a cosine identity for a sum of angles. It is shown below.
cos (A + B) = (cos A)cos B - (sin A)sin B
citation: http://library.thinkquest.org/20991/alg2/trigi.html
yerp. good stuff.