What is Trig identities: Definition and 126 Discussions

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle.
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.

View More On Wikipedia.org
Recent contents Top users
  1. S

    How Do You Simplify Complex Trigonometric Expressions?

    Theres a few... Write each expression as a single trigonometric ratio or as the number 1. 1) sint+(cott)(cost) 2) (sec x)(sin^2x)(csc x) For number one I went like this: sin t + ((1/cot)(cos/1)) sin t + (cos t/cot t) sin t + (cos t/1)( sin t/cos x) (sin t cos t)/1 + (sin t cot...
  2. W

    Why Do Fundamental Trig Identities Confuse Me?

    I just don't get this stuff. I've been trying on my own with the book. Also, is there a better way to post this? Homework Statement tanx 1 + secx _________ + _________ = 2csc x 1 + secx tanx I need to prove that this side equals the other. Homework...
  3. S

    Proving Trig Identities: Solving sin^4x + cos^4x = 1-2sin^2xcos^2x

    I'm solving a pretty descent trig identity question, but I'm stuck. I'm not going to type out the original question, but here the section that I'm stuck on: sin^4x + cos^4x and here is what I have to prove: 1-2sin^2xcos^2x I know that I'm really close, I just can't get this section. Any help...
  4. K

    Is This Trigonometric Identity Solvable?

    [SOLVED] Proving Trig Identities Homework Statement Prove that tanx - sinx---=---- tanxsinx ________------- _________ tanxsinx -------- tanx + sinx Homework Equations Is this impossible, so far it has been for me, what about you? The Attempt at a Solution I...
  5. M

    Solve X in 4.59 x 10^-4 = Sin^3(x)/Cos(x)

    Homework Statement 4.59 x 10^-4 = Sin^3(x)/Cos(x) Solve for XHomework Equations Sin(x)/Cos(x) = Tan(x) The Attempt at a Solution We can make Sin^3(x)/Cos(x) into Tan(x)Sin^2(x), but I don't think that helps... What trick do I use?
  6. R

    Trig Identities and Double Angle Formulas

    [SOLVED] Trig Identities and Double Angle Formulas Homework Statement If tan(a) = 1/5 and tan(b) = 1/239, find tan(4a - b) Homework Equations tan2x = 2tanx/1-tan^2x tan(x-y) = tanx - tany/ 1 +tanx tany The Attempt at a Solution tan (4a - b) = (tan4a - tanb)/(1 + tan4a tanb)...
  7. rocomath

    Are these trig identities correct?

    cos(90+theta) = sin(theta) sin(90+theta) = -cos(theta) cos is negative in 2nd quad sin is positive in 2nd quad i'm looking at some soln's and i just need clarification, thanks!
  8. T

    Understanding Trig Identities: Sum and Diff. & Multiple Angle

    can anyone help me understand the following and how to apply them: tig identities sum and diff. indentities multiple angle indentities I'd really appreciate it. Thanx
  9. E

    Where Can I Find a Large Trig Identities Poster for My Dorm?

    Does anyone know where I can get a nice large trig identities poster that I can put up in my dorm so I don't always have to look through wikipedia?
  10. Saladsamurai

    Proving Cosine Identity: Is cos(t+2π) the Same as cos(t)?

    \cos (t)=\cos(t+2\pi) I know it is kind of silly, but I need to do it. I could have sworn that a sum formula would have worked, ie., \cos(\alpha+\beta)=\cos \alpha \cos \beta -\sin \alpha \sin \beta but when I sub in t and 2\pi for the RHS, I am getting -\cos t Where did I go wrong...
  11. T

    Using Trig Identities to Simplify Sin(Kx)sin(2Kx)

    Could someone tell me which trig identity this chap (in a Physics textbook) is using to turn sin(Kx)sin(2Kx) into sin^2(3Kx/2) - sin^2(Kx/2) Cheers.
  12. D

    Having trouble solving Sin2x-1=0? Let's tackle it together!

    Ok this is my first post...so bear with me :smile: My problem is: Sin2x-1=0 I thought I recognized that Sin2x is from the double angle identities chapter so I substituted [2CosSin] for Sin2x. So I ended up with 2CosSin=1 ( I moved the one over) ...and then I got stuck... am I...
  13. X

    Can you help me solve this trig identity question?

    hey guyz...ok iv been trying to figure this question out for so long...and i jus can't.i get up to a certain point and then i jus get confused.so if anyone can help me that would be great! Prov that: Cos^2x + Cotx ÷ Cos^2x – Cotx = Cos^2x (tanx) + 1 ÷ Cos^2x (tanx) -1
  14. K

    How can I prove the trig identity sin2x = 2tanx/(tan^2x+1)?

    the follwing trig identity is used alot...but i am unable to proove it because i don't know wat to start with in solving it... sin2x=2tanx/(tan^2x+1) it invlves the double angle formulae i know that obviously, i tried substituting sin and cos into the RHS of equation and get my answer...
  15. K

    How Do You Prove Trigonometric Identities Involving Double Angles and Tangents?

    Hi, in this question i am nt sure the best way to tackle it! it follows proove the following 2sinxcosx=sqrt(3)-ssqrt(3)sin^2x for 0<=x<=360 i tried using the doble angle formulae on the right, putting all on one side therefore =0 (anticipating a quadratic equation) having...
  16. T

    Trig Identities Help Arrrggghhh

    Trig Identities Help...Arrrggghhh! :) I typed all of this out but the system then said I was not logged in and I lost it all...don't have time to retype everything. note: the ^ symbol is like "squared" for example, if I have 4^2 , that would be "four squared" or 4 times 4 = 16...
  17. X

    I proving two Trig identities

    1. Cos x (sec x + cos x csc^2 x) = csc^2 x I got as far as this... 1 + cos^2 + cos/sin^2 = csc^2 2. tan x(sin x + cot x cos x) = sec x
  18. K

    How Can I Simplify Trigonometric Identities for Tomorrow's Quiz?

    i had a test and i got a 55 can someone show me how to do these with the steps if possibleverify each of the folloring trigonomic identities 1) 2sin^2x - 1/sinx-cosx = sinx+cosx* did my steps wrong 2) cot^2x-cos^2x = cos^2xcot^2x didnt get an answer <no clue how to do simplify 1)...
  19. C

    Solving Trig Identities: Tips for Getting Unstuck

    I can't get anywhere with these three identities. Any tips? \frac{(\sec \theta - \tan \theta)^2 + 1}{\csc \theta(\sec \theta - \tan \theta)} = 2 \tan \theta \frac{\sin^3 \theta + \cos^3 \theta}{\sin \theta + \cos \theta} = 1 - \sin \theta\cos \theta (2a\sin \theta\cos \theta)^2 +...
  20. C

    Differentiating Trig Identities: Example

    How can I use trig identities to let me differentiate \sin \left ( x + \frac{\pi}{2} \right) and 3 \sin x - 2 \cos x?
  21. C

    (e^ix)^n=(e^ixn) & Trig identities

    ok...this was meant to be a fun problem but looks like I don't deserve to have fun! How am I meant to derive trig identities like sin(x)cos^3(x) from some complex **** like \left( {e}^{{\it ix}} \right) ^{n}={e}^{{\it ixn}}! I just don't get the idea! :cry:
  22. I

    Verifying Trig Identities help

    cos x - cos y sin x - sin y sin x + sin y + cos x + cos y = 0 or to see better i guess... (cos x - cos y)/(sin x + sin y) + (sin x - siny)/(cos x + cos y) = 0 can you guys help me? I'm really stuck on this!
  23. N

    Proving an Equilateral Triangle: Trig Identities Explained

    Trig identities please help In triangle ABC if sin (A/2) sin (B/2) sin (C/2) = 1/8 prove that the triangle is equilateral please show steps
  24. F

    How can algebra and calculus be used to derive the identity for sin(a+b)?

    How do you find the identity for sin(a+b) using algebra or calculus? I already know how to do it with geometry and by using imaginary numbers.
  25. X

    Trig Identities : Help 3 Questions.

    I can't get these 3 questions, can someone help me? 1. cotB [ (tanA + TanB) / (cotA+cotB) ] = tan A 2. (sin^2A + 2cosA - 1) / (2 + cosA - cos^2A) = 1 / (1+ secA) 3. cos^3A + sin^3A = (cosA+SinA)(1-SinAcosA) please help out on these, thanks in advance. U can write the / sign as...
  26. J

    Can You Solve These Trigonometric Identity Problems?

    Trig Identities question for test tomorrow Help! Need some help with these two problems: Thanks in advance if you could answer them: sin (X) / Cos (x) - 1 = show work Sec ^2/ cot (x) - Tan ^3x = Tan X show work to prove last one Sec x - Cos x/tanx = sinx show work to prove
Back
Top