What is Trigonometry: Definition and 660 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.

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  1. P

    Complex Algebra: Trigonometry (tan)

    Homework Statement Let tan(q) with q ε ℂ be defined as the natural extension of tan(x) for real values Find all the values in the complex plane for which |tan(q)| = ∞ Homework Equations Expressing tan(q) as complex exponentials: (e^iq - e^(-iq))/i(e^iq + e^(-iq)) The Attempt...
  2. X

    Trigonometry- addition and factor forumla

    Homework Statement If tan(A+B) = 3 and tan(A-B) = 2, find tan2A and tan2B Homework Equations tan (A - B) = (tan A - tan B)/(1 + (tan A)(tan B) and similar sort of one for tan(A+B) The Attempt at a Solution i did some calculation and got tanA= (1-2tanB)/5tanB after which there...
  3. V

    Algebra II Trigonometry Circular Functions

    Homework Statement Find the exact values of the six trigonometric function of the given number. If a function is undefined for the number, say so. 11\pi/6Homework Equations The Attempt at a Solution The way I did it was to turn it into radians by simply doing the math... 5.76 radians Then...
  4. J

    Sound attenuation barrier height (trigonometry)

    Homework Statement http://img543.imageshack.us/img543/4598/photosfr.jpg Find dss, dsr and thus hs. Homework Equations trig The Attempt at a Solution dss = hs/(sin[θ]) dsr = hs/(sin[∅]) dss = 3.059/(cos[θ]) dsr = 47.191/(cos[∅]) θ = arctan(hs/3.059) ∅ = arctan(hs/47.191) I have tried...
  5. S

    Trigonometry ( high school level )

    Cot A + Cot B + Cot C = under root 3 ABC is which type of triangle ? 1) isosceles 2) equilateral 3) right angled 4) none of these
  6. S

    MHB Prove $\prod_{r=0}^n (\cos 2^r A + \cos 2^r B)$ w/ $A,B$ Trig III

    Challenge Problem If $A=\dfrac{\pi}{2^{n+1}}$ and $B=\dfrac{\pi}{2^{n+2}}$, prove that \[\prod_{r=0}^n (\cos 2^r A + \cos 2^r B)=\frac{1}{2^{n+1}\left( \cos \frac{\pi}{2^{n+2}}-\cos \frac{\pi}{2^{n+1}}\right)}\]
  7. U

    Need hlep with a triangle question (Trigonometry)

    I'm doing some trigonometry, and right now I'm given this equilateral triangle, http://i.imgur.com/WOPCk.png So how would I go about to find side AP, AQ, and PQ? I think I have a grasp of what it is, but not sure how to execute. I know you have 60 degree angle for ABC and all sides are 3, but...
  8. S

    Understanding Trigonometric Functions: Solving for Length AD

    I need to find the length AD. I thought that with the numbers given, and angle A worked out to being 70o there would be two different ways of working length AD out. I thought 8sin20 and 8cos70 would both be acceptable ways of calculating the length but they give different values. Where have I...
  9. C

    How to change ∅ in term of x? (integration by trigonometry substitution)

    the question is ∫dx/ x^2*√(x^2-1) I use x=a sec ∅ x^2*√(x^2-1)= sec^2∅tan∅ x=sec ∅ dx= sec∅tan∅d∅ so it will become something like this ∫sec∅tan∅d∅/sec^2∅tan∅= ∫1/sec∅d∅=∫cos∅d∅ =sin∅+c But how can i change this sin in...
  10. C

    How to convert sin2∅ in trigonometry substituion.

    the question is ∫ √(y^2-25)/y^3 dy.. I did found the answer which is 1/5 sec^-1(y/5)-sin2∅/20-∅/10 But mine tutorial answer is 1/5 sec^-1(y/5)- √(y^2-25)/2y^2+c i don't know how to convert the behind part sin2∅/20-∅/10 into √(y^2-25)/2y^2
  11. A

    Solve Trigonometry Proof: A+B+C=π

    Homework Statement if A+B+C=π, prove that asin(B-C)+bsin(C-A)+csin(A-B)=0 Homework Equations sin(x-y)=sinxcosy-cosxsiny The Attempt at a Solution I tried to expand but to no avail. Any help is appreciated.
  12. nukeman

    Reviewing Trigonometry for Quadrant II: Sinθ When Cosθ = -1/4

    Homework Statement Question: Find the value of sinθ if cosθ=−1/4 and θ is in Quadrant II I have not done TRIG in a long time. Given this question, what should I read over/review ? I don't remember how to solve these types of questions? Homework Equations The Attempt at a...
  13. C

    How Far is the Ship from the Rocks When Sighting a Lighthouse?

    Homework Statement A lighthouse that rises 49 ft above the surface of the water sits on a rocky cliff that extends 19 feet from its base. A sailor on the deck of a ship sights the top of the lighthouse at an angle of 30 degrees above the horizontal. If the sailor's eye level is 14 ft above...
  14. B

    How to use trigonometry on calculator

    I know this is a pretty basic question, but it's holding me back from doing my homework due tonight. How do I use trig functions on my calculator. For example and problem in my book says: (483 N) cos (44) = 347 N When I plug it in my calculator like so: (483)cos(44) = I get: 482.9243181...
  15. M

    What Values of x Solve the Equation sin(kx) = 0?

    Homework Statement sin(kx)=0 What describes the value of x. Homework Equations N/A The Attempt at a Solution I remember doing this last year but I forgot how to. kx=n(pi) x= n(pi)/k x=n(pi)/k + (pi)k/n where n is any integar Is this right?
  16. N

    Resolving vector components using trigonometry

    Homework Statement Find the components of the vector A with length a = 1.00 and angle=20.0° with respect to the x-axis as shown. Enter the x component followed by the y component, separated by a comma. Homework Equations none The Attempt at a Solution To find the X-component...
  17. J

    Basic trigonometry question regarding knee angle

    The screen shot of the question is attached, this is apparently a basic trig question but it doesn't feel that way. Please explain as much as possible! Thanks!
  18. Feodalherren

    Trigonometry, area of triangle

    Homework Statement Use the given information to determine the area of each triangle. Two of the sides are 5cm and 7cm, and the angle between those sides is 120 degrees. Homework Equations Trig functions The Attempt at a Solution I tried drawing up a picture but it's of no help...
  19. O

    Geometry + Trigonometry Textbook

    Basically, I want a trigonometry textbook, but a lot of the texts on trigonometry use theorems in geometry as though you are already familiar with them and simply skip proofs for these theorems (such as Pythagoras theorem, some properties of triangles, properties of quadrilaterals and triangles...
  20. M

    Trigonometry and figuring out the length of the hypotenuse

    Homework Statement A monkey is chained to a stake in the ground. The stake is 2.15 m from a vertical pole, and the chain is 4.50 m long. How high can the monkey climb up the pole? The answer is given in meters
  21. A

    Trigonometry Word Problem involving Inverse trigonometric functions

    Homework Statement A ship is d feet from a dock (horizontal distance). The dock is 40 feet above sea level. The angle of depression from the dock to the ship is θ. Write θ as a function of d. Homework Equations This question is accompanied with choices. The choices are (A) θ = 40arctan(d) (B)...
  22. B

    Solve physics problem using trigonometry knowing what are you doing

    Homework Statement http://img94.imageshack.us/img94/3053/ph1d.png How does he get y_i=R-Rcos(theta)? The Attempt at a Solution if we get two triangles HBC and AHC, Rcos(theta)=AH, AB=AH+BH and AB-BH=AH=y_i.
  23. H

    Help with Trigonometry: Combine Two Triangles

    Hello Gys I have new question for you today... if u ready, let's begin http://www.mediafire.com/view/?2pp4u074ppijfbt we have two triangles, the main one is the blue the secondary is the red. if we divide the main triangle into two triangles we will get The red triangle...
  24. C

    Understanding the Simple Proof of sin^2θ = 1-cos^2θ in Trigonometry

    Hi everyone. I'm in high school still so please bear with me on the simplicity of this problem. I'm working through a calculus book and the trig intro section has a proof I know to be true, but I have a hard time following in one spot. Here it is...
  25. J

    Solving Trigonometry Equations

    Homework Statement My trig is really rusty and I've been trying to figure out why the answer is what it is: Find all solutions of the following equation: sin2 x + cos x - 1. Homework Equations Just the identity: sin2 θ + cos2 θ = 1 The Attempt at a Solution The sin2 x is in...
  26. D

    MHB Another Great Problem in Trigonometry

    If $\cos \alpha +\cos \beta + \cos \gamma=0$ and $\cos 3 \alpha +\cos 3\beta +\cos 3\gamma = \lambda \cos \alpha \cos \beta \cos \gamma$. What is the value of $\lambda$?
  27. D

    MHB A great problem in Trigonometry

    If $\sin x +\cos y=a$ and $\cos x+\sin y =b $, then what is $\tan\dfrac{x-y}{2}$ in terms of $a$ and $b$?
  28. O

    Calculating the Height of a Flagpole Using Trigonometry

    Having a fair bit of trouble with this one. Based on the answer I had thought to apply the Sine Rule but adding points to describe the lengths of elevation seems wrong, but I'm stuck on how else to approach this. Can anyone help, please? Many thanks. Homework Statement Q. A vertical...
  29. N

    MHB Trigonometry questions I'm stuck on

    Good Day, I'm stuck on two trigonometry questions. One requires me to prove a trigonometry summation and the other requires me to find the general solution of the given equation. 1. I am required to prove the b/m sin x + sin 2x + sin 3x + ... + sin nx = {sin (n/2)x sin [(n+1)/2]x}/ sin (x/2)...
  30. H

    Find the Hypotenuse of a Red Triangle - Urgent Help Needed

    Hello Guys could you please help me to find the hypotenuse for the red triangle please. regards
  31. S

    Trigonometry elementary problem

    Homework Statement If 3 sin theta + 5cos theta = 5 ... prove that 5sin theta - 3 cos theta = +- 3 Homework Equations The Attempt at a Solution i tried many things here , mostly those including squares , because i need +-3 , but this one has me stumped :/
  32. LiHJ

    Trigonometry: At which quadrant should the angle lie?

    Homework Statement Dear Mentors, I have some doubts on this question that I was doing from my textbook. Question: Given that tan A =(-2), find the exact value of sin(-A) My doubts are: For angle A to be negative, angle A should be on the 2nd or 4th quadrant. But than I will have 2...
  33. S

    Trigonometry related to Kepler's Equation

    In deriving Kepler's Equation, there's a little trig work that gets at nu (see figure), which is the true anomaly. I'm curious how the third equation makes it into the 4th (last) equation. It's been a very long time since I've played with trig. nu of course is the atan of the last equation.
  34. J

    Obtaining pi through use of trigonometry and limits

    Whilst messing around with some geometry pertaining to the n-sided regular polygon, I stumbled upon this equation which I could not find anywhere on the internet. \pi = \lim_{n \to \infty} n \sin \frac{\pi}{n} But if we take this to be true then, by substitution, this is also true: \pi =...
  35. P

    Trigonometry find the opposite side

    Hi, I'm a bit curious on how do I find the length of the Opposite side of a Right Triangle, now I have look a Soh Cah Toa, Now say if I know the length of the Adjacent Line and the the angle of the right triangle which formula should I use? I thought about Toa is this the way I solve...
  36. L

    Grade 12 Math - Trigonometry Question.

    Homework Statement tanxsinx+sinx=0 0≤x≤2∏ What is the largest domain given? Problem. I'm not sure what to do with this question. It's probably pretty simple, but I'm absolutely rubbish at math. Hopefully someone can help me with this? Thanks. -Lily
  37. P

    Multiply a trigonometry function

    Hi, I have a question I have learn a bit about trigonometry and I came across this formula angle = 38 length = 120 formula length * sin( angle ) now I have look around for the understanding about this formula and tested the formula my self...
  38. N

    MHB Optimizing Resultant Forces: Finding Maximum and Minimum Magnitudes

    Three horizontal forces of magnitudes 8N, 15N and 20N act at a point. The 8N and 15N are at right angles to each other. The force 20N makes an angle of 150 degrees with the the 8N force and an angle of 120 degrees with the 15N force. State the greatest and least possible magnitudes of the...
  39. J

    Algebra and Trigonometry by Sheldon Axler

    Hi. Anyone used this textbook? What did you think of it?
  40. N

    MHB Applications of trigonometry

    A sector of a circle, let's say AOB with circle centre O and radius 5cm has a chord subtended from A to B. This chord forms a triangle with centre 0. Angle 0 isθradians, and the area of triangle A0B is 8cm2. Given that angle AOB is obtuse, findθ. I worked out Sin-1(0.64)= 0.694, but this is...
  41. R

    Trigonometry - Which cofunction identity to use?

    Homework Statement Write the following in terms of the cofunction identity: cos(4pi/3) Homework Equations I know the θ is in Quadrant 3, but my question is, which cofunction identity am I suppose to use? Cofunction Identities: cosx = sin(pi/2 - x) #1 cosx = sin(pi/2 + x) #2...
  42. Saitama

    How Do You Solve cos(2tan-1(1/7))?

    Homework Statement cos(2tan-1(1/7)) equals- a)sin(4cot-13) b)sin(3cot-14) c)cos(3cot-14) d)sin(4cot-14) Homework Equations The Attempt at a Solution I am completely stuck in this one. I tried using the formula 2tan^{-1}x=tan^{-1}(\frac{2x}{1-x^2}). Using this formula i got...
  43. O

    Solve a Triangle using Trigonometry

    Homework Statement http://img23.imageshack.us/img23/9427/imageyakj.jpg AC+CB=24 The bisector = 8. Find angle DCB, i.e. x. Homework Equations The Law of sines, I think.The Attempt at a Solution
  44. O

    SHM: Different Final Answers When Using Energy Conversation & Trigonometry

    1. The Question from Text: "A forest playground has a tyre hanging from a tree branch. The tyre behaves like a pendulum, with a rope of 4.0 metres length, and the tyres mass 15 kg. A child of mass 45 kg swings on the tyre by pulling it 3.0 metres to one side and leaping on. What is the maximum...
  45. S

    How Do You Solve a Complex Polynomial and Trigonometry Problem?

    Homework Statement If x3 + 5x2 + 4x = 3 = 0 and cos (5 - 3x) = √p, find the value of cot (x5 + 2x4 - 6x3 + 16x2 + 8x + 20) Homework Equations trigonometry polynomial The Attempt at a Solution stuck from the beginning...:-p
  46. M

    Master Trigonometry with These Essential Practice Questions

  47. I

    Determining Lat, Long using trigonometry

    I am not sure if this is entirely possible, as my spherical trig skills are lacking. Would it be possible to determine the Lat and Long coordinates for a position on the Earth knowing the following. True North Pole is at 90°N Geomagnetic North Pole is at 82.7°N, 114.4°W Knowing the...
  48. H

    How Do You Solve sqrt(3) sec x = -2 for x in Radians?

    Find Exact Radian Solution OR to nearest 100th of a radian sqrt(3) sec x = -2
  49. B

    Trigonometry: Solving for x in cos3x = 1/2

    Hello, I'm studying for an exam and am stuck on a trigonometry question. Could anybody help me out? The question is: Solve the equation cos3x = 1/2, for x is an element of R, (where x is in radians) The answer is: x = pi/9 + 2npi/3 or x = 5pi/9 + 2npi/3 where n is an...
  50. H

    Trigonometry homework problems

    Homework Statement I need to prove that \frac{\frac{1}{2} cot20^{o}-cos10^{o}}{\frac{1}{2}+sin10^{o}}=\frac{\sqrt{3}}{3}The Attempt at a Solution I try to do it by this way \frac{\frac{1}{2}...
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