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. T

    How Does Adding π/2 Affect the Sign of Tan and Cot in Trigonometry?

    When we are given a problem to find the value of say tan(120 °), I was instructed to proceed by tan( 90*1 +30), which lies in the second quadrant and tan is negative in the second quadrant , plus odd multiple of 90 so it becomes -cot(30). Hence tan (90+α)= -cotα. But this works only because we...
  2. enter

    Getting a triangle from trigonometric function

    How can I get a right triangle from the inputs and outputs of trigonometric functions? For example: sin(x) = y The triangle would have one angle as x and the opposite edge of the triangle would be y/hyp etc. How can I get all of these values from any trigonometric function? Please tell me if I...
  3. Mastermind01

    Aversion to doing calculations

    I've developed a sort of aversion to doing huge calculations most of the time (at home) I just want to plug it into the calculator and do it . This is affecting my exams, I tend to put off questions which have a lot of calculation to do and then ultimately do the calculation wrong (We're not...
  4. K

    Dot product vs trigonometry in Gauss' law

    I'm currently writing my EP on various physical equations including Maxwell's equations, and I had to justify using the dot product of the normal unit vector and the electric field in the integral version. However, I can't think of a reason for not using trigonometry as opposed to the...
  5. Greg

    MHB Trigonometry challenge - cosine product

    Prove \cos20^\circ\cdot\cos40^\circ\cdot\cos80^\circ=\frac18
  6. Keith

    Solving a Trigonometry Problem with a Missing 90-Degree Angle

    The Attempt at a Solution I'm not sure where to start and the book doesn't show a 90 degree angle on the lower region where h meets the base. Can someone nudge me in the right direction please?[/B]
  7. J

    Geometry Beginning Trigonometry textbook

    Good morning everyone, I have written a free math textbook, and I'd appreciate some feedback on it. It's about the basics of Trigonometry, including sine, cosine, tangent, radians, the unit circle, a bit on identities, and the Law of Sines, Cosines, and Tangents. I wrote it in a rigorous...
  8. C

    Geometry Great Trigonometry and geometry books?

    Hi I'm looking for 2 books 1. a big geometry and trigonometry book that covers almost everything (also proofs) from basic to intermediate so i have a solid understanding of geometry trigonometry. 2. a geometry or trigonometry that gives you an appreciation for trigonometry fx how it was used...
  9. Byeonggon Lee

    Should I memorize all these trigonometric integrals?

    I only memorized these trigonometric differential identities : `sin(x) = cos(x) `cos(x) = -sin(x) because I can convert tan(x) to sin(x) / cos(x) and sec(x) to 1 / cos(x) .. etcAnd there is no need to memorize some integral identities such as : ∫ sin(x) dx = -cos(x) + C ∫...
  10. anemone

    MHB Trigonometry Challenge (Find x)

    Solve $\large 3^{3\cos x(1+\sin^2 x)}-3^{\cos x(4-\sin^2 x)}=6\cos 3x$.
  11. C

    Geometry Hyperbolic Trigonometry: Exploring Further with Books/Math

    My calc. 2 book more or less only mentioned the hyperbolic functions to make integration easier, so, now that I have some free time, I'd like to explore the area further. Could someone recommend a good book on the subject or do I need to take more math first? A quick google search revealed...
  12. S

    Introducing Physics First: Algebra and Trigonometry Qualifications Required

    Physics First, instead of the typically required Earth Science and Biology - Good idea, but for which students? For everybody, or just for those with enough Algebra and Trigonometry qualifications? http://en.wikipedia.org/wiki/Leon_M._Lederman
  13. noowutah

    dissecting an isosceles triangle

    Simple question, but I can't figure it out. Consider an isosceles triangle ABC with \alpha=\beta dissected by a line through C and D, where D is on AB. It is obvious that |CD|<=|AC|=|BC|, but I want to prove it using trigonometry. I can use |BD|<=|BC| in my assumptions but not...
  14. mooncrater

    Just to prove them wrong: Trigonometry

    Homework Statement There is a part of solution of a question which says that: ##cot|cot^{-1}x|=cot cot^{-1}x=x## Homework EquationsThe Attempt at a Solution If we put ##x=-1## in this equation then ##cot^{-1}(-1)=-\pi /4## which will have a modulus =##\pi /4##. And ##cot \pi /4=1## which is...
  15. A

    Tension in landing cable on an aircraft carrier

    Homework Statement [/B] Keep in mind this is a Top Gun-themed homework assignment. Cougar comes in for a shaky landing. His 20422 kg airplane traveling at 85 m/s strikes the deck at 3.5 degrees below the horizontal. Cougar's plane snags the landing cable stretched across the deck. The landing...
  16. B

    Trigonometry sin cos Question

    I know that ##\sin^2 x + cos^2 x = 1.## Is this mean that ##\sin^2 2x + \cos^2 2x = 1## or ##\sin^2 3x + \cos^2 3x = 1## or ##\sin^2 4x + \cos^2 4x = 1## and so on?
  17. shanepitts

    Function manipulation involving trigonometry

    I'm trying to integrate a function in a classical physics problem but when I apply the limits it gave undefined results. Hence, I looked up that particular part of the solution and I did not fathom the function manipulation. It states that if x≤b in the following expression...
  18. anemone

    MHB Can you prove the trigonometry challenge with angles of a triangle?

    Prove that if $A,\,B$ and $C$ are angles of a triangle, then $\dfrac{1}{\sin A}+\dfrac{1}{\sin B}\ge \dfrac{8}{3+2\cos C}$.
  19. J

    Three-dimensional trigonometry question

    Homework Statement See the document attached as it contains a diagram Homework Equations cos(theta) = adjacent/hypotenuse, sin(theta) = opposite/hypotenuse, tan(theta) = opposite/adjacent The Attempt at a Solution See document attached
  20. Prashant91

    Calculate Linear Velocity: Aircraft Direction Vector

    1.A aircraft leaves base and travels west at a speed of 100km/hr for 25 minutes, then turns right and travels north at a speed of 25m/s for 1000 seconds, then turns right and travels east at a speed of 75 km/hr for 10 minutes. The plane is asked to return to base. Determine the direction that...
  21. N

    Algebra Are There Any Good Textbooks That Teach Algebra 2 and Trigonometry Together?

    Hey PF, as my thread a week or two ago said I am currently planning on taking a college Calc and Analytic Geometry class with formal education only up to Geometry. I am very proficient in Geometry, good in algebra 1, have some experience in Trig and a little in Algebra 2. For this reason I was...
  22. ecoo

    Plus-Minus Symbol In This Trig. Equation

    Hey guys, The problem is #49 and it is a simple calculus problem, but the part that I am confused on is how the solution solves the trig. equation. In the solving, the solution brings out the plus-minus symbol and puts it outside the arccos, but I feel as if it should be inside the arccos. I...
  23. D

    Solving a Trigonometry Problem with Tan A and Tan B

    Homework Statement The lines L1 and L2 with equations y=2x and 3y=x-1 respectively,are drawn on the same set of axes. Given that the scales are the same on both axes and that the angle L1 and L2 make with the positive x-asis are A and B respectively, write down the value of Tan A and the value...
  24. Dustin11H3

    Angle/Coordinate Calculation for two "Pulley" System

    Hello everyone. This is my first post on here. I figured that I would give it a shot. Just as a quick background: I'm studying electrical engineering and I'm working an internship for a machine manufacturing company now. One of the projects I have been assigned is to come up with a system to...
  25. V

    Distance between two cities on earth

    Assume that the Earth is spherical and recall that latitudes range from 0° at the Equator to 90° N at the North Pole. Consider Dubuque, Iowa (42.50° N latitude), and Guatemala City (14.62° N latitude). The two cities lie on approximately the same longitude. Do not neglect the curvature of the...
  26. anemone

    MHB Prove: $\sin P+\sin Q> \cos P+\cos Q +\cos R$ | Trig Challenge

    Let $P,\,Q,\,R$ be the angles of an acute-angled triangle. Prove that $\sin P+\sin Q> \cos P+\cos Q +\cos R$.
  27. Futurestar33

    Range of a cannon using trigonometry?

    Homework Statement I am just stuck on a step in my problem , I have found the solution but have been attempting rearrange the equation but I just don't get it. Its probably a simple step Homework Equations 0=x[(tanα-tanθ)-(gx/2Vo^2Cos^2(α)] then this forms into this...
  28. A

    Should i take trigonometry during the summer?

    So I am a community college student and I would like to major in something within the stem field. When I arrived at cc in fall of 2014, I took my school's math placement test and scored into intermediate algebra. I wasnt satisfied with this so i went to my school's summer math academy and retook...
  29. anemone

    MHB Solve Trigonometry Challenge: $\cos^k x-\sin^k x=1$

    Solve the equation $\cos^k x-\sin^k x=1$, where $k$ is a given positive integer.
  30. physicsodyssey

    Prooving a system will travel up to 180 degrees

    Homework Statement To prove that system will travel freely upto 180 degree m2 is counterweight and m1 is mass of pan (=3kg) i have attched the fbd or another link http://www.imagebam.com/image/54bb5a394377595 Homework Equations m1(h + a sin θ) g x = m2 y h g m2 = 9.13 kg The Attempt at a...
  31. L

    Equilibrium in Two Dimensions: What Force Does a Hanging Boy Exert on Each Tree?

    Homework Statement a boy on whom the force of gravity is 400 N hangs on to the middle of a rope stretched between two trees. The rope sags in such a way that it makes an angle of 170 degrees at the boys hands. what force does the rope exert on each tree? Homework Equations F=ma The Attempt at...
  32. anemone

    MHB Trig Challenge: Solutions to $\sin a \sin (2a) \sin (3a)$?

    How many solutions does the equation $\sin a \sin (2a) \sin (3a) \cdots \sin (11a) \sin (12a) =0$ have in the interval $(0,\,\pi]$?
  33. H

    How can I accurately model a sine wave using popsicle sticks?

    I'm making a model of a sine wave out of popsicle sticks. Essentially I'm digitizing a sine wave. Let's say I'm modeling half of a cycle with ten sticks. So I need to know how long to cut each stick. So I figured it would be cos(arcsin(x/10)) for x=0 through 9. Wrong! I still can't figure...
  34. onethatyawns

    Trigonometry just the conversion factor of coordinate types?

    I think trig is assumed to be based upon triangles. This lumps trig next to squares, trapezoids, pentagons, hexagons, etc. Sure, triangles can be used to describe trig functions, but I think they do a disservice to your intuition. It's similar to Riemann sums versus integrals. True, integrals...
  35. T

    Find velocity & angle to fire cannonball through *Two* points

    At first this sounds like a very popular and often asked/solved question but it has a twist - I need help with the twist please. 1. Homework Statement A cannon is at Point A in a 3d environment. There is a wall at Point B which sits between the cannon and a castle, at Point C. Write a...
  36. X

    Finding an unknown force at an unknown angle

    Homework Statement So we have a force of unknown magnitude acting on these struts at an angle θ measured from strut AB. The component of the force acting along AB is 600lb, and the magnitude of the force acting along BC is 500lb. If Φ = 60°, what is the magnitude of F and the angle θ...
  37. W

    Trigonometry identities and equations

    1) Question statement: Simplify 2sec^2x-2sec^2xsin^2x-sin^2x-cos^2x 2)Relevant equations: tan A=sinA/cos A 1+tan^2A=sec^A cot A=1/tanA cot A=cos A/sinA sin^2A+cos^2A=1 secA=1/cos A cosecA=1/sinA 1+cosec^2A= cot^2A sin2A=2sinAcosA cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1 tan2A=(2tanA)/1-tan^2A 3)...
  38. W

    Further Trigonometry Identity (Proving question)

    1) Question: Show that (sin3A-sinA)/(cosA+cos3A)=tanA 2) Relevant equations: tan A=sinA/cos A 1+tan^2A=sec^A cot A=1/tanA cot A=cos A/sinA sin^2A+cos^2A=1 secA=1/cos A cosecA=1/sinA 1+cosec^2A= cot^2A sin2A=2sinAcosA cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1 tan2A=(2tanA)/1-tan^2A 3)Attempt...
  39. M

    Infinite series of sin + cos both to the 2n power

    Homework Statement For the following series ∑∞an determine if they are convergent or divergent. If convergent find the sum. (ii) ∑∞n=0 cos(θ)2n+sin(θ)2n[/B]Homework Equations geometric series, [/B]The Attempt at a Solution First I have to show that the equation is convergent. Both cos(θ)...
  40. M

    Solve Trigonometry Problem: 2sinx= 3x2 + 2x + 3

    Homework Statement Solve for x 2sinx= 3x2 + 2x + 3[/B] Homework Equations Lowest value of quadratic function = -D/4a (D= Discriminant) The Attempt at a Solution I have no idea how to do it
  41. Samurai44

    Trigonometry Problem: Finding sin2Ө Given sinӨ + cosӨ = 4/3

    Homework Statement sinӨ + cosӨ =4/3 ,, then sin2Ө = ... ? Homework Equations sin2Ө = 2cosӨsinӨ or any trigonometry functions... The Attempt at a Solution I tried to write sinӨ + cosӨ =4/3 in the form of cosӨsinӨ but couldn't.. is there a possible way to solve it ?
  42. Samurai44

    Trigonometry Question: Dealing with Negative and Positive Values for Theta

    In trigonometry equation (finding theta): 1) If the range of theta includes negative and positive part (such as -360<=theta<=360), and I got a value of 90,180,270 or 360.. Do I have to write the answer twice positive and negative? 2) if range of theta is positive only, and I got a negative...
  43. Euler2718

    Determining Missing Trigonometric Ratios

    I'm not stuck per say, but I need to know if I have the right idea for solving the rest of these questions. 1. Homework Statement For the following given trigonometric ratio and domain, determine the missing trigonometric ratio. Homework Equations cos\theta = -\frac{1}{2} ...
  44. Euler2718

    Trigonometry Arc Length Problem

    First I'd just like to point out that I'm taking calculus and advance pre-calculus simultaneously (kind of a stupid system) and this is a problem in the pre-calc. 1. Homework Statement 2. Homework Equations Let 'a' be arc length. a=\theta r a = \int_{a}^{b} \sqrt{1+[f'(x)]^{2}} dx...
  45. anemone

    MHB Trig Challenge: Proving $\cos^3 y+\sin^3 y=\cos x+\sin x$

    Show that if $\dfrac{\cos x}{\cos y}+\dfrac{\sin x}{\sin y}=-1$, then $\dfrac{\cos^3 y}{\cos x}+\dfrac{\sin^3 y}{\sin x}=1$.
  46. B

    Why does cos(22.5°) not equal 2/√5?

    I've never really learned any trigonometry and I'm wondering if someone could tell me where I'm going wrong here. My reasoning is this: The hypotenuse of a 1,1,√2 right triangle is at a 45° angle to its base. Halving that angle should require that the base leg be doubled if the height leg is...
  47. C

    How Can I Calculate the Height of a Building Using Right Angle Trigonometry?

    Problem was initially posted in a technical math section, so is missing the homework template. From a position 150 ft above the ground, an observer in a building measures angles of depression of 12° and 34° to the top and bottom, respectively, of a smaller building, as in the picture on the...
  48. N

    Help with law of sines/solving triangles

    Homework Statement Homework Equations SinA/a = SinB/b = SinC/c The Attempt at a Solution a=38, c=44, ∠A = 35° What I have so far: sin(35)/38 = sinC/44 44sin(35) = 38sinC 44sin(35)/38 = sinC sinC = 0.6641 sin^-1(0.6641) ∠C = 41.6º Is this ∠C1? After this I don't know how to...
  49. B

    How to Prove the Trigonometric Identities for Sin and Cos of A+B?

    Why ##\sin (A+B) = \sin A \cos B + \cos A \sin B## and ##\cos (A+B) = \cos A \cos B - \sin A \sin B## ??
  50. M

    Do I Need All Three Math Textbooks by Ron Larson?

    https://www.amazon.com/dp/1133949010/?tag=pfamazon01-20 https://www.amazon.com/dp/1285057090/?tag=pfamazon01-20 https://www.amazon.com/dp/1133959741/?tag=pfamazon01-20 So I'm planning on buying the books in the links above (Algebra and trig, precalc and calc by Ron Larson), but as they are...
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