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.
We’ve already learned the sum/difference identities of sine and cosine: cos(alpha +/- beta)=cos alpha cos beta -/+ sin alpha sin beta sin(alpha +/- beta)=sin alpha cos beta +/- cos alpha sin beta Although we haven’t learned tangent, it is tan(alpha +/- beta)=tan alpha +/- tan beta / 1-/+tan alpha tan beta
These identities can be used to find the exact values of trigonometric functions when the angle can be written as the sum or difference of two special angles.
Along with sum/difference identities , there are double and half angle identities. Double angle formulas are: sin(2 alpha) = 2sin(alpha)cos(alpha) cos(2 alpha) = cos squared(alpha) – sin squared(alpha) cos (2 alpha) = 2 cos squared (alpha) -1 cos(2 alpha) = 1-2 sin squred(alpha) tan (2 alpha) = 2 tan(alpha) / 1- tan squared(alpha) *** You'll notice that there are several listings for the double angle for cosine. That's because you can substitute for either of the squared terms using the basic trig identity sin^2+cos^2=1
The double and half angle formulas can be used to find the values of unknown trig functions. For example, you might not know the sine of 15 degrees, but by using the half angle formula for sine, you can figure it out based on the common value of sin(30) = 1/2. They are also useful for certain integration problems where a double or half angle formula may make things much simpler to solve. Also, the double angle formulas are used to derive the power-reducing formulas. Knowing the sum/difference and double/half angle identities make solving much more easier.
This week we have started off learning some of the angle identities. These types of formulas are helpful when you need to simplify expressions with trigonometric functions. The most common technique used is the substitution rule, although, there are a few ways to use these formulas.
So far, we have already learned the sin and cosine identities, and we went over tan and cot a little bit. These types of problems get tricky because you need to know your identities and the trig chart in order to do good with this.
Sum and Difference Formulas: Sin( A + B) = sinAcosB + cosAsinB Sin( A – B)= sinAcosB – cosAsinB Cos(A + B)= cosAcosB –sinAsinB Cos(A – B)= cosAcosB + sinAsinB Tan(A+ B)= tanA+tanB/1- tanAtanB Tan( A – B) = tanA- tanB/ 1+ tanAtanB
So far we have learned the sum and difference of sine and cosine. Working these problems are very easy if you know your identities and the trig chart. All it consists of is replacing formulas to solve the equation. COSINE: cos(alpha +/- beta)=cos alpha cos beta -/+ sin alpha sin beta SINE: sin(alpha +/- beta)=sin alpha cos beta +/- cos alpha sin beta
DOUBLE ANGLE FORMULAS: sin2alpha=2sinalpha cos alpha cos2alpha=cos^2 alpha-sin^2 alpha
HALF ANGLE FORMULAS: sin alpha/2= +/- square root of 1-cos alpha/2 cos alpha/2= +/- square root of 1+cos alpha/2
**there are also tangent formulas but we have not went over those yet. DOUBLE: tan2alpha=2tan alpha/1-tan^2 alpha HALF: tan alpha/2=1-cos alpha / sin alpha= sin alpha // 1+cos alpha
The double and half angle formulas are used to make solving problems easier. All you need to do is learn your formulas and youre good to go.
We began learning some of the angle identities this week. These formulas can be useful when you need to simplify expressions with trigonometric functions. The substitution rule,is the most common technique used with these formulas, although, there are a few ways to use these formulas.
Since Mondey, we have already been taught the sin and cosine identities, and have touched on tan and cot a little bit, along with section 10-3 today. You must know your identities and the trig chart in order to do good with these problems, or they can become kind of tough.
Sum and Difference Formulas: Sin( A + B) = sinAcosB + cosAsinB Sin( A – B)= sinAcosB – cosAsinB Cos(A + B)= cosAcosB –sinAsinB Cos(A – B)= cosAcosB + sinAsinB Tan(A+ B)= tanA+tanB/1- tanAtanB Tan( A – B) = tanA- tanB/ 1+ tanAtanB
Starting this week we learned the angle identities for sine and cosine or sum/difference identities of sine and cosine. These formulas are used to simplify trigonometric functions and find the exact values of them. All you have to do is use the substitution rule, which means replacing the formulas and know your trig chart to solve them. Referring back to chapter 8 you will need to know your identities as well. Your calculator will not help you at all with these problems. Double Angle Formulas for Sine, Cosine, and Tangent:
In class this week we learned learned Double/ Half angle identities. We also learned the sum/differences formulas. These formulas will be important because as Mrs. Robinson stated in class we will either make an A or an F in this chapter. To make an A we must study our formulas, if not we will make an F(;. That is why its important to know the sum/differences formulas and Double/Half angle identities in the present. We will also need these formulas in the future.
These formulas are used to simplify trigonometric functions and find the exact values of them. All you have to do is use the substitution rule, which means replacing the formulas and know your trig chart to solve them. Referring back to chapter 8 you will need to know your identities as well. Your calculator will not help you at all with these problems. Double Angle Formulas for Sine, Cosine, and Tangent: Formulas: Sum and Difference Formulas: Sin( A + B) = sinAcosB + cosAsinB Sin( A – B)= sinAcosB – cosAsinB Cos(A + B)= cosAcosB –sinAsinB Cos(A – B)= cosAcosB + sinAsinB Tan(A+ B)= tanA+tanB/1- tanAtanB Tan( A – B) = tanA- tanB/ 1+ tanAtanB Double Angle Formulas: Sin2A = 2sinAcosA Cos2A = cos^2 A- sin^2A = 1- 2sin^2A =2cos^2 A-1 Tan2A = 2tanA/ 1-tan^2A Half Angle Formulas: Sin(1/2A) = +/- square root 1-cosA/2 Cos(1/2A)= +/- square root 1+cosA/2 Tan(1/2A) = 1-cosA/sinA = sinA/1+ cosA
So far we have learned many formulas with identities. Sum and Difference Identities- Sine & Cosine: cos(alpha +/- beta)=cosacosb -/+ sinasinb sin(alpha +/- beta)=cosacosb +/- sinasinb Tangent: tan(alpha + beta) = tana+tanb/1-tanatanb tan(alpha - beta) = tana-tanb/1+tanatanb cot(alpha + beta) = 1-cotacotb/cota+cotb
When you know each formula it makes it easier to work each problem. Especially when you have the half angles it is a way to work out the problems with decimals.
In class, This week we learned about sum/difference and Double/Half angle Identies formulas in chapter 10. The key to performing well on these ch.10 quizes is knowing your trig chart and applying the trig chart to help you solve the problems.It mainly consists of plugging in the formulas.
We’ve already learned the sum/difference identities of sine and cosine:
ReplyDeletecos(alpha +/- beta)=cos alpha cos beta -/+ sin alpha sin beta
sin(alpha +/- beta)=sin alpha cos beta +/- cos alpha sin beta
Although we haven’t learned tangent, it is tan(alpha +/- beta)=tan alpha +/- tan beta / 1-/+tan alpha tan beta
These identities can be used to find the exact values of trigonometric functions when the angle can be written as the sum or difference of two special angles.
Along with sum/difference identities , there are double and half angle identities.
Double angle formulas are:
sin(2 alpha) = 2sin(alpha)cos(alpha)
cos(2 alpha) = cos squared(alpha) – sin squared(alpha)
cos (2 alpha) = 2 cos squared (alpha) -1
cos(2 alpha) = 1-2 sin squred(alpha)
tan (2 alpha) = 2 tan(alpha) / 1- tan squared(alpha)
*** You'll notice that there are several listings for the double angle for cosine. That's because you can substitute for either of the squared terms using the basic trig identity sin^2+cos^2=1
Half angle formulas are:
sin(alpha/2) = +/- square root (1-cos alpha) / 2
cos(alpha/2) = +/- squre root (1+cos alpha) / 2
tan(alpha/2) = 1-cos alpha / sin alpha = sin alpha / 1+cos alpha
The double and half angle formulas can be used to find the values of unknown trig functions. For example, you might not know the sine of 15 degrees, but by using the half angle formula for sine, you can figure it out based on the common value of sin(30) = 1/2. They are also useful for certain integration problems where a double or half angle formula may make things much simpler to solve.
Also, the double angle formulas are used to derive the power-reducing formulas.
Knowing the sum/difference and double/half angle identities make solving much more easier.
http://www.freemathhelp.com/trig-double-angles.html
http://wps.prenhall.com/esm_blitzer_algtrig_2/13/3560/911519.cw/index.html
This week we have started off learning some of the angle identities. These types of formulas are helpful when you need to simplify expressions with trigonometric functions. The most common technique used is the substitution rule, although, there are a few ways to use these formulas.
ReplyDeleteSo far, we have already learned the sin and cosine identities, and we went over tan and cot a little bit. These types of problems get tricky because you need to know your identities and the trig chart in order to do good with this.
Sum and Difference Formulas:
Sin( A + B) = sinAcosB + cosAsinB
Sin( A – B)= sinAcosB – cosAsinB
Cos(A + B)= cosAcosB –sinAsinB
Cos(A – B)= cosAcosB + sinAsinB
Tan(A+ B)= tanA+tanB/1- tanAtanB
Tan( A – B) = tanA- tanB/ 1+ tanAtanB
Double Angle Formulas:
Sin2A = 2sinAcosA
Cos2A = cos^2 A- sin^2A
= 1- 2sin^2A
=2cos^2 A-1
Tan2A = 2tanA/ 1-tan^2A
Half Angle Formulas:
Sin(1/2A) = +/- square root 1-cosA/2
Cos(1/2A)= +/- square root 1+cosA/2
Tan(1/2A) = 1-cosA/sinA = sinA/1+ cosA
http://en.wikipedia.org/wiki/List_of_trigonometric_identities
http://www.regentsprep.org/Regents/math/algtrig/ATT14/formulalesson.htm
So far we have learned the sum and difference of sine and cosine. Working these problems are very easy if you know your identities and the trig chart. All it consists of is replacing formulas to solve the equation.
ReplyDeleteCOSINE: cos(alpha +/- beta)=cos alpha cos beta -/+ sin alpha sin beta
SINE: sin(alpha +/- beta)=sin alpha cos beta +/- cos alpha sin beta
DOUBLE ANGLE FORMULAS:
sin2alpha=2sinalpha cos alpha
cos2alpha=cos^2 alpha-sin^2 alpha
HALF ANGLE FORMULAS:
sin alpha/2= +/- square root of 1-cos alpha/2
cos alpha/2= +/- square root of 1+cos alpha/2
**there are also tangent formulas but we have not went over those yet.
DOUBLE:
tan2alpha=2tan alpha/1-tan^2 alpha
HALF:
tan alpha/2=1-cos alpha / sin alpha= sin alpha // 1+cos alpha
The double and half angle formulas are used to make solving problems easier. All you need to do is learn your formulas and youre good to go.
http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Double-.2C_triple-.2C_and_half-angle_formulae
We began learning some of the angle identities this week. These formulas can be useful when you need to simplify expressions with trigonometric functions. The substitution rule,is the most common technique used with these formulas, although, there are a few ways to use these formulas.
ReplyDeleteSince Mondey, we have already been taught the sin and cosine identities, and have touched on tan and cot a little bit, along with section 10-3 today. You must know your identities and the trig chart in order to do good with these problems, or they can become kind of tough.
Sum and Difference Formulas:
Sin( A + B) = sinAcosB + cosAsinB
Sin( A – B)= sinAcosB – cosAsinB
Cos(A + B)= cosAcosB –sinAsinB
Cos(A – B)= cosAcosB + sinAsinB
Tan(A+ B)= tanA+tanB/1- tanAtanB
Tan( A – B) = tanA- tanB/ 1+ tanAtanB
Double Angle Formulas:
Sin2A = 2sinAcosA
Cos2A = cos^2 A- sin^2A
= 1- 2sin^2A
=2cos^2 A-1
Tan2A = 2tanA/ 1-tan^2A
Half Angle Formulas:
Sin(1/2A) = +/- square root 1-cosA/2
Cos(1/2A)= +/- square root 1+cosA/2
Tan(1/2A) = 1-cosA/sinA = sinA/1+ cosA
http://en.wikipedia.org/wiki/List_of_trigonometric_identities
http://www.regentsprep.org/Regents/math/algtrig/ATT14/formulalesson.htm
and our Math Notes.
Starting this week we learned the angle identities for sine and cosine or sum/difference identities of sine and cosine. These formulas are used to simplify trigonometric functions and find the exact values of them. All you have to do is use the substitution rule, which means replacing the formulas and know your trig chart to solve them. Referring back to chapter 8 you will need to know your identities as well. Your calculator will not help you at all with these problems.
ReplyDeleteDouble Angle Formulas for Sine, Cosine, and Tangent:
Sin(α +/- β) = (sin α) (cos β) +/- (cos α) (sin β)
Cos(α +/- β) = (cos α) (cos β) -/+ (sin α) (sin β)
Tan2α = 2tan α/1- tan2 α
Half Angle Formulas for Sine, Cosine, and Tangent:
Sin α/2 = +/- square root of 1 - cos α/2
Cos α/2 = +/- square root of 1 + cos α/2
http://en.wikipedia.org/wiki/List_of_trigonometric_identities
http://www.freemathhelp.com/trig-double-angles.html
This comment has been removed by the author.
ReplyDeleteIn class this week we learned learned Double/ Half angle identities. We also learned the sum/differences formulas. These formulas will be important because as Mrs. Robinson stated in class we will either make an A or an F in this chapter. To make an A we must study our formulas, if not we will make an F(;. That is why its important to know the sum/differences formulas and Double/Half angle identities in the present. We will also need these formulas in the future.
ReplyDeleteThe Double angle formulas are:
Sin2A = 2sinAcosA
Cos2A = cos^2A – sin^2A
Cos2A = 2 cos^2A -1
Cos2A = 1-2 sin^2A
Tan2A = 2 tanA / 1- tan^2A
The Half Angle Formulas are:
Sin(1/2A) = +/- square root 1-cosA/2
Cos(1/2A)= +/- square root 1+cosA/2
Tan(1/2A) = 1-cosA/sinA = sinA/1+ cosA
The Sum and Difference Formulas are:
Sin( A + B) = Sin(A)Cos(B) + Cos(A)Sin(B)
Sin( A – B)= Sin(A)Cos(B) – Cos(A)Sin(B)
Cos(A + B)= Cos(A)Cos(B) –Sin(A)Sin(B)
Cos(A – B)= Cos(A)Cos(B) + Sin(A)Sin(B)
Tan(A+ B)= Tan(A)+Tan(B)/1- Tan(A)Tan(B)
Tan( A – B) = Tan(A)- Tan(B)/ 1+ Tan(A)Tan(B)
Sources: John's Thoughts and Math Notes
These formulas are used to simplify trigonometric functions and find the exact values of them. All you have to do is use the substitution rule, which means replacing the formulas and know your trig chart to solve them. Referring back to chapter 8 you will need to know your identities as well. Your calculator will not help you at all with these problems.
ReplyDeleteDouble Angle Formulas for Sine, Cosine, and Tangent:
Formulas:
Sum and Difference Formulas:
Sin( A + B) = sinAcosB + cosAsinB
Sin( A – B)= sinAcosB – cosAsinB
Cos(A + B)= cosAcosB –sinAsinB
Cos(A – B)= cosAcosB + sinAsinB
Tan(A+ B)= tanA+tanB/1- tanAtanB
Tan( A – B) = tanA- tanB/ 1+ tanAtanB
Double Angle Formulas:
Sin2A = 2sinAcosA
Cos2A = cos^2 A- sin^2A
= 1- 2sin^2A
=2cos^2 A-1
Tan2A = 2tanA/ 1-tan^2A
Half Angle Formulas:
Sin(1/2A) = +/- square root 1-cosA/2
Cos(1/2A)= +/- square root 1+cosA/2
Tan(1/2A) = 1-cosA/sinA = sinA/1+ cosA
http://en.wikipedia.org/wiki/List_of_trigonometric_identities
So far we have learned many formulas with identities.
ReplyDeleteSum and Difference Identities-
Sine & Cosine:
cos(alpha +/- beta)=cosacosb -/+ sinasinb
sin(alpha +/- beta)=cosacosb +/- sinasinb
Tangent:
tan(alpha + beta) = tana+tanb/1-tanatanb
tan(alpha - beta) = tana-tanb/1+tanatanb
cot(alpha + beta) = 1-cotacotb/cota+cotb
Double angle formulas:
Sin2A = 2sinAcosA
Cos2A = cos^2A – sin^2A
Cos2A = 2 cos^2A -1
Cos2A = 1-2 sin^2A
Tan2A = 2 tanA / 1- tan^2A
Half Angle formulas:
Sin(1/2A) = +/- square root 1-cosA/2
Cos(1/2A)= +/- square root 1+cosA/2
Tan(1/2A) = 1-cosA/sinA = sinA/1+ cosA
When you know each formula it makes it easier to work each problem. Especially when you have the half angles it is a way to work out the problems with decimals.
In class, This week we learned about sum/difference and Double/Half angle Identies formulas in chapter 10. The key to performing well on these ch.10 quizes is knowing your trig chart and applying the trig chart to help you solve the problems.It mainly consists of plugging in the formulas.
ReplyDeleteDouble Angle:
Sin2A=2sinAcosA
Cos2A=cos^2A-sin^2A
Cos2A=2cos^2A-1
Cos2A=1-2sin^2A
Tan2A=2tanA/1-tan^2A
Half-Angle Formulas
Sin(1/2A) = +/-square root1-cosA/2
Cos(1/2A)= +/-square root1+cosA/2
Tan(1/2A) = 1-cosA/sinA=sinA/1+ cosA
The Sum and Difference Formulas are:
Sin( A + B) = Sin(A)Cos(B) + Cos(A)Sin(B)
Sin( A – B)= Sin(A)Cos(B) – Cos(A)Sin(B)
Cos(A + B)= Cos(A)Cos(B) –Sin(A)Sin(B)
Cos(A – B)= Cos(A)Cos(B) + Sin(A)Sin(B)
Tan(A+ B)= Tan(A)+Tan(B)/1- Tan(A)Tan(B)
Tan( A – B) = Tan(A)- Tan(B)/ 1+ Tan(A)Tan(B)
Source:Wikipedia..and the chapter notes that i suprisingly took