What is Trigonometry: Definition and 655 Discussions

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine.Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation.Trigonometry is known for its many identities. These
trigonometric identities are commonly used for rewriting trigonometrical expressions with the aim to simplify an expression, to find a more useful form of an expression, or to solve an equation.

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

    Mastering Trigonometry Equations: Solving for Missing Solutions in [0,2π)

    1.) sin2x=3cos2 2.) (3tan2x-1)(tan2x-3)=0 3.) cos3x=cosx 4.) 3tan3x=tanx Those were a few of the problems in the section I missed on friday due to illness and I was wondering if anyone could walk me through them. Would be greatly appreciated! They want to solve the equation for...
  2. E

    Trigonometry in this calculus problem

    Find all the points on the graph of the function f(x) = 2 \sin x + \sin^2 x at which the tangent is horizontal. f'(x) = 2 \cos x + 2 \sin x \cos x = 0 2 \cos x (1 + \sin x) = 0 \cos x = 0 or \sin x = -1 x = \frac{\pi}{2} + n\pi or x = \frac{3\pi}{2} + 2n\pi I then plug into find the...
  3. C

    Having trouble getting this trigonometry problem started

    The problem is Solve sin(2y)=cos(4y) for y, where \\0\leq y \leq 360 This one is tricky, I want to try to equate either sin to cos or cos to sin so I can work with only one trig function, but how? I don't see how to start this problem. I know that the period of sin2y is 720deg or 4pi, and...
  4. A

    Finding Angle A in a Circular Arc: A Physics Trigonometry Problem

    Hello, I am currently in beginning physics and we are learning a lot about Trig onometry. A homework problem is really bugging me. Here's what it says: Find the angle A, given the altitude and arc length of the figure shown: (the picture is in the attachment and also some work i have done.)
  5. Orion1

    What is the simplified trigonometry procedure?

    Because Trigonometry is a pre-requisite for Calculus, the purpose of this procedure is for use in 'calculator banned' Calculus courses, to eliminate the requirement of memorizing sixteen 'special angles' in Trigonometry to derive the correct solution. Memorizing this procedure can produce all...
  6. P

    Trigonometric Identities for Solving for Exact Values

    hey i have a problem which I am puzzled over. i I am given that: \sin A = \frac{3}{5} and i am asked to find exact values for: \sin 2A \cos 2A \tan 2A where 90^0 \leq A \leq 180^0 (the power to zero is the degree sign) i have gone about solving this by the use of a pythagorien (?) triple...
  7. P

    How can I prove the trigonometry identity \sin^4 - \cos^4 = 1 - 2\cos^2?

    i need to prove the following identity \sin^4 - \cos^4 = 1 - 2\cos^2 i have tried approaching this identity by solving the RHS (right hand side) of the equation but this lead no where. however i am unsure on how to maniplulate the LHS of this equation because of the power of 4. would...
  8. Orion1

    Trigonometry integration

    Is it possible to integrate a trigonometry function within a function, or is this a formula that cannot be integrated in terms of elementary functions? \int \sin(\cos x) dx
  9. A

    Pleas help exam tommarow Trigonometry word problems

    Pleas help! exam tommarow! Trigonometry word problems Hi, i really need help with this question, on a wall, a spider is 100cm above a fly. the fly starts moving horizontally at the speed of 10cm/s. After 1s, the spider begins moving at twice the speed of the fly, in such a way as to...
  10. N

    Complicated trigonometry problem

    Could someone check this for me and help answering the questions at the end The 3 angles around point 6 are 120 degrees each. This is also the case for point 8 which is linked to point 2, 3 and 7. Now the 3 angles formed by the lines leaving point 7 are also 120 degrees. If the distance...
  11. H

    Help Solving a Trigonometry Problem - Questions Welcome!

    Hello, I'm brand new here; needless to say, I think it's great what this community is doing. Now to my question: my class is just finishing up geometry, which means we're starting to enter into beginning trig. Here's the problem: 1-Sinx/1+Sinx = (Secx-Tanx)^2 So far, I've been able...
  12. L

    Can Trigonometry Be Applied to Circles with a Radius Other Than 1?

    I understand how trigonometry is related to the Unit Circle, but is there any way I can relate the same concept to circles with a radius other than 1? Thanks in advance. :biggrin:
  13. P

    A diff. eq. or trigonometry related problem?

    y' = 2y/x + x cos (y/x^2), with y=z*x^2 => y' = 2zx + x cos z and y=z*x^2 => y' = 2zx + x^2 * dz/dx So that leaves x^2 * dz/dx = x cos z => dz/cos z = dx/x I integrate both sides so that: sec z + tan z = x + C But I don't have a clue on how to get past that point. Should I start...
  14. G

    Trigonometry made more rational

    Trigonometry made more "rational" I read an article the other day on "rational trigonometry" and decided to go exploring... and I feel as if a lightbulb has turned on. This seems like such a wonderful new technique to doing otherwise cumbersome problems, and I agree that it does feel like a...
  15. R

    What are some non-Java interactive websites for trigonometry?

    I recently was given an assignment to find three interactive websites that refer to sine, cosine, and tangent. This wouldn't be a problem... if it weren't for the fact that the laptops they are required to run on do not have Java, and cannot load the applets. I need the URLs for these sites by...
  16. J

    Solve Quadrilateral Angle Given 4 Side Lengths & 1 Angle

    I have reduced a problem I am trying to solve to something simpler though rather difficult: Four side lengths and an angle uniquely describe a quadrilateral, solve one of the angles adjacent to the one given. No matter what algebraic / trigonometric manipulations I apply I cannot get a...
  17. D

    How Did Trigonometry Functions Originate and Evolve?

    How would you, to the best of your abilities, explain to someone like me how trigonometry functions emerged? I'm not in any way or form an advanced mathematics student and in this specific subject I only know the basics of the very basics (i.e how to find the sides and angles of right...
  18. J

    Who discovered Trigonometry?

    I have read that astronomers are responsible for much of the advances in trig hundreds of years ago but never seem to find who exactly pioneered this field of research.
  19. D

    Solving Trigonometry Problems Without a Calculator

    im trying to remember how to do some trig. first of all, how do you find cos^-1 (5/3) without using a calculator? 2nd, i need help proving this identity: 2sin^2(x) - cos (x) - 2 sin (x) + 1 = 0 3rd, how do you evaluate sin 165 (which is sin (11/12 pi)) again without using a...
  20. M

    Trigonometry without sines cosines or tangents?

    http://physorg.com/news6555.html :!) :!) :!) :!) :!) could this be the second coming?
  21. R

    An end to classical trigonometry?

    http://physorg.com/news6555.html Discuss.
  22. Pythagorean

    New Trigonometry Method: Quadrance and Spread

    I haven't been here for a long time, so sorry if this was already posted: http://physorg.com/news6555.html Dr Norman Wildberger has devised a new method of trigonometry that gets rid of sin, cos, tan (and the like) functions and uses algebra instead. It's supposedly straight forward, more...
  23. T

    Equivalent Expression for Cot 50 Degrees

    How do I go about finding the equivalent expression for cot 50 degrees? When I work the problem, I come up with tan 130 degrees. Where am I going wrong?
  24. T

    Need Help with Trigonometry Homework | Simplifying cos2xsin2x-cos2x

    I am having extreme difficulty with my Trigonometery homework. In particular, When I simplify the expression: cos2xsin2x-cos2x I come up with cos2x. This is obviously incorrect. Where am I going wrong?
  25. R

    Trigonometry slope problem .

    I am really stumped! Using only Trigonometry, I am suppose to calculate the amount of force that is needed to keep a 2000 lb car from rolling down a ramp of 30 degrees. Am I on the right track when I say: x=2000cos 30? Then what?
  26. G

    How can I solve this 3D trigonometry question involving a river and a post?

    I'm really struggling with the following question: A river running due east has straight parallel banks. A vertical post stands with its base, P, on the north side of the river. On the south bank are two surveyors, A who is to the east and B who is to the west of the post. A & B are at a...
  27. Y

    Fundamentals of Trigonometry (No Graphing/Inverse Trig)

    it was a one semester class, so it is basic. note: i will not cover graphing and inverse trig function. i will begin by introducing a unit of measurement of angles, because i find them much easier to work with. that unit is radian. the name will make sense after the description. we have a...
  28. M

    How to solve cos7pi/6 in baby steps?

    Can someone break down in "baby steps" how to solve the following?: cos7pi/6=? thank you. :uhh:
  29. D

    Understanding Trigonometry: Explanation of the Inverse Tangent Function

    I have a straight-forward question. Could anybody please explain me why... \theta = \tan ^{-1} \left( \frac{x}{2} \right) \Rightarrow -\frac{1}{4\sin \theta} = -\frac{\sqrt{x^2+4}}{4x} Thanks
  30. honestrosewater

    Trigonometry book like Euclid's Elements?

    I'm looking for a trigonometry book that is rigorous, concise, insightful, etc. Something along the lines of Euclid's Elements, Spivak's Calculus, Rudin's Principles. I understand it's usually taught at the high school or college freshman level, but I'd like a book that someone who already knows...
  31. S

    Proving Trigonometric Identity: 1-cos2x+sin2x = tanx/1+cos2x+sin2x

    Hi everyone, I'm sorry to bother you with such a trivial question but I really am stuck here. I don't know why I can't prove this one as I've managed to get harder ones than this, but as it is I need help with it. This is the question: Prove 1-cos2x+sin2x = tanx...
  32. L

    Functions, Statistics, and Trigonometry problem

    I've been stuck on this question for awhile. Q: Square numbers 1, 4, 9, 16, 25... are the values of the function s(n)=n^2, when n is a positive integer. The triangular numbers t(n)=(n(n+1))/2 are the numbers t(1)=1, t(2)=3, t(3)=6, t(4)=10. Prove: For all positive integers n, s(n+1) = t(n)...
  33. M

    Trigonometry Preparing for math contest; Please help

    Prove that the triangle ABC is: a) acute, if and only if tan(alfa)*tan(beta)>1 b) right, if and only if tan(alfa)*tan(beta)=1 c) obtuse, if and only if tan(alfa)*tan(beta)<1
  34. W

    Do I need to study trigonometry before calculus?

    I am studying calculus on my own, and I just skip everything to do with trigonometry. I have never done trigonometry before(except just the basic ratios), and I was wondering whether you really need to study trigonometry before calculus. I see a lot of trigonometry in my calculus book, and I...
  35. M

    Finding the inside angle using trigonometry

    I'm new to trigonometry, but I think I know the basics - soh cah toa ect. If I want to find the angle of the pendulum first then I need to do: Sin-1 * (opp / hyp) However I haven't got the hypotenuse, but the adjacent. So am I right to firstly work out the hypotenuse by opposite2 +...
  36. S

    Finding the Magnitude and Direction of a Force Vector Using Trigonometry

    A force vector F1 points due east and has a magnitude of 200N. A second force F2 is added to F1. The resultant of the two vectors has a magnitude of 400N and points along the east/west line. Find the magnitude and direction of F2. i really don't know what equation I would use to solve this...
  37. M

    Trigonometry Question from a Math Contest

    sin^8(x) + cos^8(x) = 97 / 128
  38. A

    Right angle triangle trigonometry

    The question says determine theta I have a triangle with a hypotenuse of 3 cm opposite the angle theta is 2cm length and adjacent to that is unknown. I don't know how to solve this question I don't remember what theta is lol or how to punch it in the calculator what do I do please help...
  39. J

    Supplementary Angles for Spherical Trigonometry

    I'm trying to review spherical trinometry on my own and I'm stuck where it says the supplement of the solved dihedral angle can be implemented. I'm using "PLANE AND SPHERICAL TRIGONOMETRY" by Paul Rider. Can anyone explain the concept behind that statement, because the examples that I have are...
  40. F

    Help me prove this Trigonometry identity

    Someone pls help me prove this identity. I'm going nuts :confused: tan^2x - sin^2x = tan^2x sin^2x
  41. S

    Solving a Basic Trigonometry Doubt: Where to Learn?

    I have basic trignometry doubt how to u get 5cos(2t-53.13degrees) from 3cos2t + 4 sin2t. Can someone suggest a site from where I can lean basic trinometry thanks. skan
  42. A

    Solving Angle X with Sin(x/2)=1/2 & Tan(x)=sqrt(3)

    find the angle x if its known that: sin(x/2) = 1/2 tan(x)=sqrt(3) 0<=x<=360
  43. P

    Solving for Triangle Angle with Known Side Measurements | Trigonometry Question

    Well, does anyone know how to solve for an angle of a triangle if you already have the measurements of all three sides? Any help would be appreciated.
  44. 4

    Trigonometry sin cos tan Question

    How do I do this? Thanks.
  45. A

    Are SEC and CSC functions only used in English?

    hello everyone, well my story is a bit complicated.. since I've entered school i was french educated, now I'm in my last year and I'm moving to an english school and I'm in the field GS (general sciences) the reason for moving schools is that I'm traveling to Canada next year to study...
  46. X

    Trigonometry Obscurity: Solving Triangle ABC

    Hey everyone, I was looking over some old pre-calculus exams and I found this rather obscure looking question.. It's about trigonometry. You're given a triangle ABC, and the legs are a (BC),b (AC), c (AB). You're given the lenghts of a=5, b-8, and the angle C between them is 140. The...
  47. C

    Solving cos^-1 (3/7): Exact Trigonometric Values and Techniques

    Hello all In my textbook I encountered the following problem: Find the six trigonometric values of cos^ -1 (3/7). They must be exact. I gather what they mean is that I find arccos (3/7). I tried applying basic identities, but didn't work. Any help would be appreciated. Thanks
  48. K

    Trigonometry identity proof trouble. (Help much appreciated)

    I can do pretty much all the proofs except these two, though I've tried to make a start. Note that in the questions the angle is given as theta, but for the sake of my keyboard I've changed it to angle 'x'. Q15: Prove: Tan2xsecx = 2sinxsec2x. So I need to show the two sides are equal...
  49. denian

    Trigonometry homework help question

    in triangle PQR, PQ = a, QR = a + d, RP = a + 2d, and angle PQR is more than 120 degree., where a and d are positive constants. show that 2a/3 < d < a. i tried to think, but i really don't know how to start to solve this question. hope for some clue. thank you
  50. M

    I've created some new formulas in trigonometry (perhaps)

    Hi all, I'm a newbie here and sorry for my bad English. I want to share with you guys 2 formulas I've created luckily on a boring day: 1) Let R be circumscribed circle of triangle ABC, let S be it's area. We have: S=2R^2*sinAsinBsinC 2)Let S be area of triangle ABC, a=BC, b=CA, c=AB. We...
Back
Top