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.

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  1. M

    Is Tan 43° Exactly Equal to (sqrt(5) - 1)/2?

    Homework Statement Show that the exact value of tan°43' is \frac{\sqrt{5}-1}{2} Homework Equations The Attempt at a Solution tan2x = \frac{2tanx}{1-tan^{2}x} \frac{2tan31° 43}{1-tan^{2}31° 43'} From here, i got stuck or I'm doing it wrongly, i forgot how to do it...
  2. M

    Trigonometry - How to solve this equation and find the solutions.

    Solve: sin^2x = (sinx)(cosx) 0 < x < 2pi Find exact solutions. Okay, so I got 0, pi/4, but just wasn't sure how to do this... I know you bring the sinxcosx to the other side, making it sin^2x - sinxcosx = 0 ...and then I tried factoring out sinx leaving me with sinx(sinx -...
  3. D

    Analytic Trigonometry: Solving Equations in (0, 2∏) Interval for cos(2x)=1/2

    Homework Statement Find all the solutions of each equation in the interval (0, 2∏) cos(2x)=1/2Homework Equations -None- The Attempt at a Solution cos(2x)=1/2 2x=(cos^(-1))*1/2 2x= ((∏)/3), ((5∏)/3) 2x= ((∏)/3), ((5∏)/3), ((14∏)/6) x= ∏/6, ((5∏)/6), That's all I have. I know there is one...
  4. L

    Solving Trigonometry Problem: sin θ / √1-sin^2 θ

    1. sin θ / √1-sin^2 θ I don't know this, I know sin = 1 / csc but I not sure how to do this problem :( I don't know about the √1-sin^2 θ
  5. M

    Question on E gravitational potential , but my doubt is regarding trigonometry more.

    In this question 3 bi http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9702%20-%20Physics/9702_w07_qp_2.pdf to find gravitaional poteintial enrgy we need to find Δh. which is the vertical difference between the two spheres shown in the diagram. How do i find that? Answer...
  6. Z

    Solving for a: A Tricky Trigonometry Problem

    Homework Statement Is there a way to solve this for a? \frac{r\sin a}{t - r\cos a} = \cos \theta r\sin a=t\cos \theta - r\cos a \cos \theta Homework Equations The Attempt at a Solution I am not that good with trig...this isn't a homework problem but since it is like one it belongs here. My...
  7. B

    Why do trigonometry angles go counter-clockwise?

    The idea of a circle divided into 360 degrees that goes clockwise has been around for thousands of years (see orienteering compasses). So, why do radians and angles in trigonometry go counter-clockwise and start off pointing to the right? Was that on purpose?
  8. M

    Trigonometry Question (Trigonometric Functions)

    Homework Statement Hello again, not looking for anyone to solve this problem this time I just need to know what the operation I'm supposed to do is called, so I can go research it and learn it. If sin(t) = -12/13 with 3pi/2 < t < 2pi, find the following: b) cos(t - 11pi/6) Homework...
  9. X

    Trigonometry: arctan equation?

    Can someone please let me know how to find x in π/4=arctan(x+arctan(x+...)) ?
  10. G

    Trigonometry and method of difference

    Homework Statement Given that 1+2cosx+2cos2x+2cos3x + ....+2cosnx = sin(x+1/2)x cosec(x/2) Prove that 1-2cosx+2cos2x-2cos3x+....+2cos8x = cos(17/2)x sec(x/2) Homework Equations The Attempt at a Solution 1+2cosx+2cos2x+2cos3x + ....+2cos8x = sin(8+1/2)x cosec(x/2)...
  11. C

    Finding Vector Components using Trigonometry

    [PLAIN]http://img832.imageshack.us/img832/449/physicsu.png By c42711 at 2011-10-30 I am supposed to find the X and Y components of the above vector. What I tried to do first was dot in a line, forming a triangle. I then tried to find the length of that line using tangent. I got 431.8, but I...
  12. Z

    What is the meaning of grade in Trigonometry?

    Hi, I'm here to just ask a simple question: What is "grade" in Trig? I have been presented the question: "A bus traveled up a road that had a grade of 15%. What angle does this correspond to, what ratio and what slope is this?" I have not made an attempt on this question because I don't...
  13. R

    Simple trigonometry / geometry question. Diagram included

    Hey all, BACKGROUND: (please note that knowledge of this is not necessary): I'm currently writing a javascript application using vectors (with jquery and raphaeljs) that enables me to rotate custom text (using font.js file, not normal fonts). However, due to a bug in the new version of raphael...
  14. P

    Trigonometry - half angles problems

    Homework Statement Previous part of the question I have solved: Express cos(2x) in terms of sin(x): I got this answer: cos(2x)=1-2sin2(x) Hence or otherwise solve the equation cos(x) + 3sin(x/2) = 2 Homework Equations Double angle formulae: cos(2x)=cos(2x) - sin(2x)...
  15. M

    Can You Prove This Trigonometry Equation?

    I'm new to this forum, anyhow thanks for the admin making such forum, doesn't matter ! I've been trying this calculation for one day still no answer, Homework Statement cos (A/2)+cos (B/2)+cos (C/2)=4cos [(B+C)/4]*cos [(C+A)/4]*cos [(A+B)/4] A+B+C = pi Homework Equations The Attempt at a...
  16. M

    Solving a Trigonometry Question: Rate of Change from pi to 11pi/6

    Hey guys I am new in this forum so if i posted this question in the wrong section, please notify me. Anyway. My concern here is this. So I am trying to find the RATE OF CHANGE of f from pi to 11pi/6 f(x)= tan x I have attached the part i need help on. Note: This is very simple but...
  17. K

    Question involving trigonometry & river currents

    1. A man points his rowboat north from A to B, straight across a river of width 100 m. The river flows due east. The man starts across, rowing steadily at 0.75 m/s and reaches the other side of the river at point C, 150 m downstream from his starting point. What is the speed of the river...
  18. K

    Question involving the mathematics of physics and trigonometry

    I am having trouble solving this question, please help and show work! Thank you! A boat that can travel at 4.0 km/h in still water crosses a river with a current of 2.0 km/h. At what angle must the boat be pointed upstream (that is, relative to its actual path) to go straight across the...
  19. T

    Prove or Disprove: (n\Pi+\Pi/2)+n\Pi=(2n+1/2)\Pi

    Homework Statement Prove or disprove the following equation. (n+\pi/2)+n\pi=(2n+1/2)\pi n=0,1,2,3... Homework Equations None. The Attempt at a Solution I have simplified the equation to this form, I just need help proving it. Thanks in advance.
  20. Darth Frodo

    Oblique Collision Trigonometry problem

    Homework Statement A smooth sphere collides with an equal sphere which is at rest. Before the impact the line of motion of the first sphere makes an angle A with their line of centers, after the impact this is angle B. The coefficient of restitution is 1/4. Show that 8TanA = 3TanB Homework...
  21. C

    Solve Max of sin(x) + sin(2x): Get Answer Now!

    This is not homework question, just curious about it though. This problem is supposed to be done without a computing device and was in an exam at a university course. I don't think it can be done. Homework Statement I want to find the maximum of this function: Y = sin(x) + sin(2x) Homework...
  22. B

    Trigonometry Textbook - Get Prepared for Calculus

    Hey everyone! I want to study trigonometry thoroughly without having to take the course, mostly since I'm taking Precalculus this semester and I'll be learning most of the principles of trigonometry in this course. I want to study it carefully so that I can get myself better prepared for...
  23. Saitama

    What is the value of n in the identity sin^3xsin3x=\sum^n_{m=0}{}^nC_mcosmx?

    Homework Statement Suppose sin^3xsin3x=\sum^n_{m=0}{}^nC_mcosmx is an identity in x, where C0, C1, ...Cn are constants, and Cn \neq0, then what is the value of n? Homework Equations The Attempt at a Solution I expanded the sigma notation and got:-...
  24. F

    Why Do We Convert Degrees to Radians in Trigonometry?

    Homework Statement Well basically I'm trying to learn trigonometry from a textbook. It shows a rule, to change from degrees to radians, multiply by pi/180. to change from radians to degrees, multiply by 180/pi . Homework Equations The Attempt at a Solution I'm the type of...
  25. H

    Is Taking Trigonometry Again Beneficial?

    I wasn't sure what to title this thread, so I apologise if it is misleading. I took trigonometry in high school and remember the fundamental things (unit circle, identities, sohcahtoa, right triangles, the law of sines, cosines, etc.). I have been able to handle trigonometry in calculus...
  26. D

    Trigonometry Help: Proving 1-cos@ / sin@ = tan(@/2)

    Homework Statement will sum1 prove this ...@=theta 1-cos@ / sin@ = tan(@/2)Homework Equations The Attempt at a Solution i tried to do this cos@ = cos^2(@/2) - sin^2 (@/2) wat now? ... thats doesn't get me anywhere
  27. P

    A simple book on trigonometry?

    First of all, sorry if I posted in the wrong category (it happened with the last topic I made, all this names are confusing :D ). I made this topic because I don't know trigonometry. Just a few notions (like the formula of sin,cos,tan). But I also hate it a lot. And because learning is...
  28. L

    Trigonometry reflection problem

    Hi, I was about solving a refrection problem and I'm just one step away from the solution. I stuck at some simple problem I guess. I have: \alpha=60°+\frac1 3 arcsin(\frac1 {1,33} sin(\alpha)) and I want to find the alpha but I have troubles to solve this. I guess it's not that...
  29. M

    Trigonometry, find the minimum of tan(a).tan(b).tan(c)

    Homework Statement 1. Given a,b,c are acute angles and a + b + c =180. find the minimum of tan(a).tan(b).tan(c) 2. Prove that if a+b+c=90, then tan(a)+tan(b)+tan(c) >= 31/2 Homework Equations The Attempt at a Solution I don't even have any ideas how should i start to find/prove them... any...
  30. M

    Trigonometry, find cos(a-b)

    Homework Statement Given that sin(a) + cos(b) = 31/2/2 and sin(a) + sin(b) = 3/2 Find cos(a-b) Homework Equations The Attempt at a Solution Can anyone give me some hints?
  31. J

    How do I get from #2 to #3 in this trigonometry identity problem?

    I'm working on some trigonometry identity problems, and I'm stuck on this particular problem. This is how it is shown in the solution, but I cannot see how to get the highlighted part. Any help on how to get from #2 to #3 (the highlighted) is very much appreciated Jesper
  32. M

    Trigonometry - compound angels

    Homework Statement Evaluate http://img828.imageshack.us/img828/3383/msp588119g042f0f3ba0368.gif without using calculator or tables. Homework Equations The Attempt at a Solution I have no ideas how tan37 and tan23 can be found... can anyone give me some hints? The answer given...
  33. D

    Spherical Trigonometry question

    Im trying to use spherical trig to solve a problem In the standard method to compute the angles, I already have only the following four angles A, a, B, b but from these, how can I compute either C, or c? Thanks
  34. N

    Simple Inverse trigonometry question

    This is a simple question but I really need to know why: why is the alternate form of arccosh(x) = log(x + sqrt(x^2 - 1)) and not log(x - sqrt(x^2 - 1)) How do I justify the plus/minus sign? I need to know this ASAP, thanks.
  35. J

    Maximum and Minimum in Trigonometry

    Homework Statement Find Maximum and Minimum value of Homework Equations \mathbf{f(x) = sin^{2n+1}\; x - cos^{2n+1}\; x} and \mathbf{n\in\mathbb{N}} The Attempt at a Solution put \mathbf{n=1, f(x) = sin^3\; x -cos^3\; x}\\\\ get \mathbf{-1\leq f(x)\leq 1}
  36. J

    How Is Trigonometry Used to Calculate Forces on an Arrow's Bottom Beam?

    How would I calculate the force acting on the bottom beam in the arrow shown? http://www.flickr.com/photos/the_other_shots/5726954751/
  37. B

    Why are the functions y= cos x and y = sin(x+90) considered the same function?

    1. Explain why the functions y= cos x and y = sin(x+90) are the same function. Explanation must be detailed include graphs if you wish. 2. Outline why the identities are referred to as Pythagorean identities: sin²θ + cos²θ = 1 1 + tan²θ = sec²θ 1 + cot²θ = csc ²θ HELP...
  38. O

    What is the exact value of sin when cos x =1/√10?

    Homework Statement cos x is a first quadrant angle in standard position and cos x =1/√10 . Find the exact value of sin . Homework Equations ? The Attempt at a Solution ?
  39. P

    Calculate the height Trigonometry

    Hi A surveyor is attempting to calculate the height of a Point P, on a building by taking measurements on a horizontal level ground. From a point A, the angle of elevation of P is 30 degrees. He then advances 20 m towards Point P, Point B, and measures an angle of elevation of 45 degrees...
  40. K

    How Do You Calculate the Radius and Surface Area of a Cone Formed from a Sector?

    1) A piece of paper is in the shape of a sector of a circle. The radius is 8cm and the angle at the centre is 3pi/4 radians. The straight edges of the sector are placed together so that a cone is formed. Show that the base of the cone has a radius of 3cm. Find the area of theh curved surface of...
  41. D

    Trigonometry Limits: Solving lim x -> 0 sin x / sin(x/2)

    Homework Statement Find lim x -> 0 \frac{sin x}{sin\frac{x}{2}} The Attempt at a Solution Since period of sin 2(x/2) is T/2 compared to period T of sin (x/2) sin 2(x/2) nears twice the value of sin (x/2) for all values of x approaching zero. Therefore lim x -> 0 \frac{sin...
  42. P

    Understanding the Unit Circle and Trigonometry Functions

    I am learning about the unit circle and I am a bit confused. So, I have my circle drawn with radius 1 and I sketched a right angled triangle inside it so that the hypothenuse has a length of 1. I think what is making me confused is the meaning of sine, cosine and tangent. They are...
  43. A

    Trigonometry Engineering Waves proble

    Homework Statement Hi I am doing a maths past paper and I would like some help to understand where part of the solution came from. The part I do not understand is the bit at the end which says tan\alpha = 5\pi/4. It would be great if someone could help me understand where this came from...
  44. T

    Trigonometry Proof: Proving Sin^8 + Cos^8 = (a+b)^3

    Homework Statement Given the equality \frac{sin^4(x)}{a} + \frac{cos^4}{b} = \frac{1}{a+b} Prove that : \frac{sin^8(x)}{a^3} + \frac{cos^8}{b^3} = \frac{1}{(a+b)^3} The Attempt at a Solution I cubed on both the sides of the 1st equation and solved a bit, reaching no where. Then I...
  45. C

    How to Solve Tan(x) = 3 Without Calculator: Trigonometry Question

    This is no homework exercise, just plain curiosity for an exercise, so give it lower priority. Homework Statement Is it possible to solve tan(x) = 3 without the use of a calculator? The knowns: 1) It originaly came from trying to solve 1/(cos^2) -2tan = 4. 1 = cos^2+sin^2 so this...
  46. M

    Solve Mcos^2(x) + Ncos(x) – 3 = 0 for M & N | Trig Help

    Homework Statement If cos(x) = -¾ or cos = ½ then the value of M and N in the equation Mcos^2(x) + Ncos(x) – 3 = 0 are what? Homework Equations Identities I can use: csc(x) = 1/sin(x) cot(x) = 1/tan(x) sec(x) = 1/cos(x) tan(x) = sin(x)/cos(x) cot(x) = cos(x)/sin(x) sin^2(x)...
  47. M

    Solve Trigonometry Proofs: Tan(x) – ½sin(2x) = tan(x)sin2(x)

    Homework Statement I need help with trigonometry proofs. the question asks me to prove the following and show all my steps. Prove that: Tan(x) – ½sin(2x) = tan(x)sin2(x)Homework Equations I don't know :( The Attempt at a Solution No attempt as I don't get it.Any help at all would be...
  48. 1

    Am I right, what's your opinion? trigonometry

    a=4, b=1, C=120* do you agree, that if you do not round until the final amswer, that angle B = 10.90? rounded to the nearest hundredth? correct answer given is 10.92...
  49. J

    The difference between precalculus and trigonometry?

    OK at the 2 year college here, they offer ONLY trig , and you take that after college algebra, and before you take calculus, and the counselors at the 2 year college all say that, trig and precalculus mean the same thing there, which is weird, because, then if you look at the classes offered at...
  50. N

    What is the relationship between trigonometry and physics?

    How big of a role does trigonometry play in physics? I am learning trigonometry as of this instance and I'm finding it to be incredibly interesting and fascinating.
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