Trig identities Definition and 126 Threads

Homework Statement The two vectors a and b lie in the xy plane and make angles α and β with the x axis. a)By evaluating a • b in two ways (Namely a •b = abcos(θ) and a • b = a1b1+a2b2) prove the well-known trig identity cos(α-β)=cos(α)cos(β)+sin(α)sin(β) b)By similarly evaluating...

Hello, Say I'm working with ∫ sqrt(1-cos(t)) dt I end up with a substitution of u = 1-cos(t) and dt = du/sin(t) sub back in: ∫ sqrt(u) / sin(t) du Still got a t in there ... hrrmmm So I go to wolfram alpha for some inspiration and 'show steps'...

Homework Statement This isn't really a problem that was assigned to me, (I'm studying independently) I just have a question about the general concept behind some identities. Homework Equations sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b) sin(theta) = sin(180-theta) The...

I know you can derive the double angle formulas for sin(2a) and cos(2a) from Euler's identity, but is there any way to derive the tan(2a) in a similar manner from an easier formula? What about the addition/subtraction formulas (i.e. sin(a+b), etc.)

Homework Statement Find the exact value of: sin (-5∏/12) 2. The attempt at a solution sin (-45° + -30°) = sin -45° cos -30° + cos -45° sin -30° = (sqrt (2) / 2 )(sqrt (3) / 2 ) + (sqrt (2) / 2)(1 / 2) = (sqrt (6) + sqrt (2)) / 4 However, the book has (-sqrt (6) -...

Homework Statement Use fundamental identities to simplify the expression: (sinx)^2 - (cosx)^2 ____________________ (sinx)^2 - (sinx cosx)*note: it's a numerator and denominator. The underscore line is the fraction line. *note: The answer in the back of the book is "1 + cotx" but I would...

Hello! I've been tackling the question 'Express sin3x+sinx as a product and hence solve 1/2(sin3x+sinx)=sin2x ; x∈R' but I'm stumped - I'm not sure whether I've even approached it correctly. This is what I did: sin(3x+x)=sin3x.cosx+sinx.cos3x inserting this into the second equation...

Homework Statement Suppose c and (1 + ic)^{5} are real, (c ≠ 0) Show that either c = ± tan 36 or c = ± tan 72The Attempt at a Solution So I considered the polar form \left( {{\rm e}^{i\theta}} \right) ^{5} and that \theta=\arctan \left( c \right) , so c = tan θ Using binomial expansion, I...

Homework Statement Use Euler's identity to prove that cos(u)cos(v)=(1/2)[cos(u-v)+cos(u+v)] and sin(u)cos(v)=(1/2)[sin(u+v)+sin(u-v)] Homework Equations eui=cos(u) + isin(u) e-ui=cos(u)-isin(u) The Attempt at a Solution I was able to this with other trig identities with no...

Homework Statement (3/5)cos2x + (3/5)sin2x The Attempt at a Solution I would think the answer would be 6/5, but it looks like the book is saying 3/5. I had a similar problem to this the other day and I tried finding it in my history but I couldn't.

Please, check my work. Homework Statement a) Show that sqrt{[1+tan^2x]/[1+cot^2x]}=tanx b) Show that [cosx+sinx]/[cosx-sinx]=1+[2tanx]/[1- tanx] c)Show that cotxcosx+tanxsinx=(cosecx+ secx)(1-sinxcosx) d) Show that cosec^2x-cosecx=cot^2x/[1+sinx] e) Show that sin^3x-cos^3x=...

Hello all, I'm wanting to learn how to derive all of the trig identities (well, not all, but the most common) rather than memorizing them. Perhaps someone here could provide me with a list of "essentials" that are the framework for deriving others. For example, I know there are a few that can...

How do you do stuff like sin(pi/4) in your head or sin(1) or sec(pi(x))? Thanks for your help. I'm in Calc II and fully understand the calculus but my trig foundation from high school isn't the best.

I am currently taking Calc II and we are doing trig substitutions at the moment. I seem to have forgotten almost all the important trig identities. I understand that this sounds like something I should google but I honestly cannot find a good list of the trig identities I should know at this...

Homework Statement \int\frac{sec^{2}x}{tan^{4}x}dxHomework Equations The Attempt at a Solution I have the answer as -1/3 cot^3(x) + C listed. All the intermediate steps are given, but the first one is they have converted the sec/tan integral in to: \int{cot^{2}x}{csc^{2}x} dx I am a little...

Homework Statement tan^2x - sin^2x = sin^2x*tan^2x Homework Equations The Attempt at a Solution This is how my teacher solved it. Sin^2x sin^2x ______ - ______ Cos^2x 1 sin^2x - cos^2x*sin^2x _________________________ cos^2x = sin^2x (1-cos^2x)...

Homework Statement Prove this identity m) Sin^2 x / sin^2 x + cos x^2 = tan^2 x / 1 + tan^ x Homework Equations http://i52.tinypic.com/105tdtk.jpg Letter (m) on the top The Attempt at a Solution I don't know to much about trig identities, he barely taught anything. But...

My book was proving that.. sin(-x) = -sin(x) tan(-x) = -tan(x) cos(-x) = cos(x) .. I posted an attachment of the books explanation.. I just don't understand how their explanation has anything to do with sin of a negative angle equaling sin of an angle times negative one, the same goes for...

Homework Statement ArcTan(-1) = theta I figured that theta was both 7pi/4 and 3pi/4.. but the book has -pi/4 Because my two answers are both equivalent to -pi/4 would I be wrong? Homework Equations The Attempt at a Solution

Homework Statement x=2acos(theta- pi/3)cos(theta) y=2acos(theta- pi/3)sin(theta) Write everything in terms of x and y Homework Equations cos(a-b)=cos(a)cos(b)+sin(a)sin(b) sina/cosa=tana etc... The Attempt at a Solution I've tried a lot of rearranging, can't figure it out.

Tan theta=sin theta/cos theta What does that identity mean? What does it say about the triangle? And what on Earth is an identity? I understand everything taught in the course so far, trig ratios, reciprocal trig ratios, special angles etc etc...but i have no idea what identities mean, some...

Homework Statement Problem 6. If you know that tan(theta) = -4/5 and sin(theta) > 0, find: (a) sin(theta) (b) cos(theta) (c) tan(theta + pi)Homework Equations cos^2(t)+sin^2(t)=1 tan(t)=sin(t)/cos(t) The Attempt at a Solution My teacher went over this today, but likes to skip over steps that I...

When formally proving trig identities using algebra are you allowed to divide? Ordinarily I wouldn't think twice about this. Sure, the trig function by which you are dividing might take on 0, but not for all angles. We divide by potential zeros all the time. My advisor was being very coy...

Homework Statement I have been practicing proving trig. ident. for the past couple of days... although I am getting better... I wanted to ask are there any strategies that I should be aware of to make the process easier ? Homework Equations The Attempt at a Solution

Proving trig identities I have 2 more this time, thanks for the time! Homework Statement -sin^2x-sin^2y+1=cos(x+y)cos(x-y) Homework Equations Compound, double, pythagorean, reciprocal, quaotient, etc. The Attempt at a Solution R.H.S. cos(x+y)cos(x-y) =...

Homework Statement integrate: sin (2x)/(1+sinx) Homework Equations (sin x)^2 + (cos x) ^2 = 1 sin (2x) = 2 sin x cos x cos (2x) = (cos x)^2 - (sin x)^2 The Attempt at a Solution I've been trying to integrate this thing for about an hour by rearranging various trig...

Homework Statement sin^3(x)-cos^3(x) sin(x) - cos(x) equals 1 + sin(x) + cos(x) Homework Equations Not sure :/ The Attempt at a Solution Not sure where to even start.

[b]1. How do I prove sinxcosxsec^2x=tanx Homework Equations sec^2x = tan^2x + 1 The Attempt at a Solution sinxcosx(tan^2x + 1) tan^2xsinxcosx +sinxcosx sin^2x/cos^2x*sinxcosx + sinxcosx - is this valid? I'm not sure what I've done is even correct - but it doesn't seem...

Homework Statement 1/cscx-sinx = secx tanx Homework Equations cscx = 1/sinx secx = 1/cosx The Attempt at a Solution 1/cscx-sinx = secx tanx L.S. = 1/cscx-sinx = 1/(1/sinx)-sinx R.S. = secx tanx = (1/cosx)(sinx/cosx) This is where I'm getting confused. Why can't...

Homework Statement How to get from \sqrt{2+2cosx} to 2cos(x/2) The Attempt at a Solution I'm pretty much stuck on this. I can only see that is simplifies by taking out the common factor 2, which isn't correct.

Homework Statement Verify that each equation is an identity- directions Problem- csc(A-B)=secB ---------------- <<< divide bar sinA-cosAtanB Homework Equations well i tried to put in terms of sin cos and I've gotten stuck The...

Homework Statement 1. cos θ - 1 / cos θ = sec θ - sec^2 θ 2. (sin θ + cos θ)^2 = 1 + 2 sin θ cos θ 3. (1 / 1 + cos θ) + (1 / 1 - cos θ) = 2csc^2θ Homework Equations 1 / cos θ = sec θ 1 / sin θ = csc θ sin^2 θ + cos^2 θ = 1 cos^2 θ = 1 - sin^2 θ sin^2 θ = 1 - cos^2 θ...

cos(x-(pie/2))=cos(x)tan(x) I have to verify this identity and can't seem to figure it out. cos (x-y)=cos x * cos y + sin x * sin y well since cos y = 0, it kind of eliminates that side of the equation and I end up with sinx * sin1 Did I go about this all wrong?

Homework Statement Prove Trig. Identities 1. sec θ (sec θ - cos θ)= tan^2 θ Homework Equations sec θ = 1/cos θ tan θ = sin θ/ cos θ cot θ = cos θ / sin θ The Attempt at a Solution 1. sec θ * sec θ - sec θ * cos θ 1/ cos θ * 1/ cos θ - 1/ cos θ * cos θ ----> cos θ is...

Homework Statement Cos^2x-Sin^2x/2 SinxCosx The Attempt at a Solution I changed cos^2x to 1- sin^2x which then the equation was 1- s sin^2x/2snxcosx and i have no idea how to make this a single trig. function

Homework Statement This is actually many steps through a calculus problem involving trig functions. I have not included the problem because I'm trying very hard to figure it out on my own (at least as far as it's possible). I've found the answer I'm looking for, but it's attached to a bunch...

How do I prove that (1+sin2x) = (cosx) (cosx + sinx) (cosx - sinx)

Can someone please help me with these two questions. Th first one is prove: 1-tan^2x ________ = cos2x 1+tan^2x & the second one is prove: sinx+ sinxcot^2 = secx

Ok guys, here's my problem. I left on vacation with my parents before I learned how to do these correctly. I have been trying and I sort of have the gist of them down. For instance, tan A*sec A simplified is sin A. A=theta. But as I move on they stop making sense, and this is where my problem...

Homework Statement By using trig formulas show that, sin(2x + pi/3) = sin(2x) + sin(2(x+pi/3)) Homework Equations Trig Identities The Attempt at a Solution I've used double angle formulas, sin(a+b) formulas, I just can't seem to get it.

Homework Statement for homework we have to find 2 different dirrivatives of the same problem (one may be incorrect) and then tell if they are equal 2. The attempt at a solution original y=sec(x)*cot(x) the two derrivatives (i know these are correct becase i have compared with others in...

[tan(pi/4+x)-tan(pi/4-x)]/[tan(pi/4+x)+tan(pi/4-x)]=2sinxcosx I tried to prove this trig identity but I an really stuck. I think tan of pi/4 is '1', and if I do that then my numerator becomes zero, thus zero=2sinxcosx. But that can't be right, so I don't know what to do now. LS=...

Homework Statement I'm not looking for anyone's pity, but I can't even begin to tell you how confused I am with this concept. My teacher spent all of five minutes teaching it to us and then leaves us to fend for ourselves with this ridiculously hard worksheet. Please help. 1. 2cscx =...

Homework Statement The problem is essentially (I've rephrased it, but this is what it is asking) show that [ (2n1cosa) / (n2cosa + n1cosb) ]2 is equal to (sin2a sin2b) / (sin2(a+b)cos2(a-b)) where these are for refraction through materials and satisfy n1sina=n2sinb 2. The...

I was wondering if anyone could help me out about trig identities. I'm a HS trig teacher and I'm going "by the books" and instructing them to manipulate the left and right sides of the identity independently of each other. They are not to treat it like an equation, e.g. no moving terms from...

Everyone knows the obvious trig identities like sin^2 + cos^2 =1, cosx=1+ sin^2, and tanx =sin/cos. I ran across an old identity the other day: 3cos^2(3x)+3sin^2(3x)=3. Can anyone here figure out why and how? I tried it and couldn't figure it out.

Hi Helpers:blushing:, the following is my problem: I have to rearrange Equation(1) to make Equation(2) using trigonometric identities (1): E(θ)=2Eo + (ΔR)^2 (c(x)cos^2(θ-θo) + c(y)sin^2(θ-θo)) (2): E(θ)=2Eo + ½(ΔR)^2 ((c(x)-c(y))cos(2(θ-θo)) + (c(x) + c(y)) I was able to get...

Hi, I'm confused about using trig identities. Homework Statement Match the trigonometric function with one of the following: (a) -1, (b) cos(x), (c) cotx (d) 1, (e) -tan(x), (f) sin(x) (1-cos^2x)(cscx) Homework Equations None that I know of. The Attempt at a Solution I multiply it...

exam coming up...need some help with these identities for practise. prove the following: A) \frac{tan^3x}{1+tan^2x}+\frac{cot^3x}{1+cot^2x}=\frac{1-2sin^2xcos^2x}{sinxcos} B) sec^6x-tan^6x=1+3tan^2xsec^x C) cos^4x=\frac{3}{8}+\frac{1}{2}cos2x+\frac{1}{8}cos4x D)...

Hi all Teacher gave me homework that i am having trouble doing it .. i need help in these two problems which i can't seem to solve. how can i prove the following : @= theta sec@ + tan@ = tan@sec@ cot@ + cos@ and sin^2@ - tan@= tan^2@ COS^2@ - cot@ my try is...