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. C

    Question about trigonometry proofs

    1) Are there any proofs that sine cosine and tangent are the same in all similar triangles? Like, that sine 30 degrees is the same no matter what the lengths are? Or is it just an axiom? 2) Is there a proof for the actual value for the sine cosine and tangent ratios (besides for common ones...
  2. T

    Trig Right triangle Trigonometry

    Homework Statement As ship is anchor off a long straight shoreline that runs north and south. From twi observation points. 15 miles apart on shore the bearings of the ship are N 31 ° E and S 53 ° E. What is the shortest distance from the ship to the shore. Homework Equations Sin θ Opp/...
  3. MarkFL

    MHB Aju051000's questions at Yahoo Answers involving trigonometry

    Here are the questions: I have posted a link there to this topic so the OP can see my work.
  4. E

    Basic Engineering Mechanics (trigonometry)

    Homework Statement Two forces P and Q are applied to the lid of a storage bin as shown (see picture). Knowing that P = 48N and Q = 60N, determine by trigonometry the magnitude and direction of the resultant of the two forces. Homework Equations "The triangle method" where you put each...
  5. K

    How to Solve Trigonometry Exercises with Unknown Information

    Hi, I'm trying to start studying trig. again and I found some types of exercises that i have no idea how to solve can someone point me in the right direction? Sorry for the image size. In the first one I'm supposed to find the length of the smallest square knowing that the other two are 6 cm...
  6. M

    Simplifying a trigonometry expression

    Homework Statement Simplify: [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x Homework Equations none The Attempt at a Solution [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x [(sec x)(sec2 x) - tan x (1 -1) sec x ] / sec2 x [(sec x)(sec2 x) - 0 ] /...
  7. M

    Dimensional anaylsis problem involving trigonometry

    Homework Statement Dimensional Analysis: A displacement is related to time as: x = A sin (2∏ft), where A and f are constants. Find the dimensions of A. (Hint: a trigonometric function appearing in an equation must be dimensionless.) Homework Equations t = seconds The domain of a sine...
  8. L

    Solution to Trig Homework: Show $\dot{\phi} = -2m\gamma v \sin{\frac{\phi}{2}}$

    Homework Statement \phi = 4\arctan{\exp^{m\gamma(x-vt)}} Show \dot{\phi} = -2m\gamma v \sin{\frac{\phi}{2}} Homework Equations The Attempt at a Solution \phi = 4\arctan{\exp^{m\gamma(x-vt)}} \tan{\phi/4} = \exp^{m\gamma(x-vt)} \frac{\dot{\phi}}{4\cos^{2}{\frac{\phi}{4}}} =...
  9. Saitama

    Inverse trigonometry - Finding solutions

    Homework Statement Which of the following is the solution set of the equation $$2\arccos(x)=\text{arccot}\left(\frac{2x^2-1}{2x\sqrt{1-x^2}}\right)$$ A)(0,1) B)(-1,1)-{0} C)(-1,0) D)[-1,1] Ans: A Homework Equations The Attempt at a Solution I start by rewriting LHS in terms of ##\arctan##...
  10. Saitama

    Infinite series - Inverse trigonometry

    Homework Statement The sum of the infinite terms of the series \text{arccot}\left(1^2+\frac{3}{4}\right)+\text{arccot}\left(2^2+\frac{3}{4}\right)+\text{arccot}\left(3^2+\frac{3}{4}\right)+... is equal to A)arctan(1) B)arctan(2) C)arctan(3) D)arctan(4) Ans: B Homework Equations The Attempt at...
  11. paulmdrdo1

    MHB Trigonometry problem-belt driven pulley

    A pulley with a radius of 10 inches uses a belt to drive a pulley with a radius of 6 inches. Find the angle through which the smaller pulley turns as the 10-inch pulley makes one revolution. State your answer in radians and also in degrees. can you rephrase the question for me. thanks!
  12. QuantumCurt

    Gelfand's Trigonometry: Reviews & Deeper Understanding

    Hey everyone, I was wondering if anyone had any thoughts on Gelfand's Trigonometry book. https://www.amazon.com/dp/0817639144/?tag=pfamazon01-20 I'm looking for a trigonometry supplement. I actually just finished taking trig over the summer, but my textbook(Larson's Trigonometry) does a...
  13. S

    MHB Review my solution: Trigonometry proof

    For a triangle with sides a, b, c and angle C, where the angle C subtends the side c, show that c \geqslant (a+b) \sin \left( \frac C2 \right) _______ Let us stipulate 0^\circ < C < 180^\circ and of course a,b,c > 0. Consequently, 0^\circ < \frac C2 \leqslant 90^\circ \implies 0 < \sin^2...
  14. H

    Trigonometry Algebraic problem

    Hello, Could you please help me with a problem that I saw in my exam? I have tried to solve it but end up getting one solution which is not correct. There happens to be 2 solutions to the problem which appear periodically. The problem has to be algebraically solved without the use of a...
  15. J

    What is the proof for the sum formula for sines?

    I don't need unit circle proof or proof using trignometric equality. I know those. I am attaching a image. Please read it. It is from the book Plane Trigonometry by S L Loney. See what it says. I know that angle MOP = angle M'P'O and both triangles formed are congruent, OM' = MP and M'P" = OM...
  16. rakeru

    Pre-Calculus and Trigonometry

    Hi! I am currently taking a math class called college algebra. Here's the little description thing: MAC1105 - This course introduces the student to the concept of functions and their graphs. Students will graph linear, quadratic, rational, exponential, logarithmic, radical, power, and...
  17. F

    Basic Trigonometry - Phasor Diagram

    Homework Statement Hello everyone, I am having difficulty with something that should be very basic knowledge for most engineers here. I cannot see how this trigonometric relationship is being made from the phasor diagram I attached... I remember the SohCahToa rule, but it's just not...
  18. J

    Trigonometry Word problem with angles of elevation

    Homework Statement An Antenna that is 90 feet high is on top of a hill. From a point at the base of the hill, the angles of elevation to the top and bottom of the antenna are 28.5° and 25°, respectively. To the nearest whole number of feet, how high is the hill? A, 189 ft B, 213 ft C...
  19. T

    Good Algebra 2 and Trigonometry Study Method?

    I want to learn algebra 2 and trigonometry and was going to try to learn algebra 2 first then learn trigonometry after that. However after thinking I thought it would be more engaging to learn both at the same time. So my question is, should I learn algebra 2 first, then trigonometry, or...
  20. W

    Trigonometry (Further Maths)

    Verify the compound angle formulae for; a) sin (20° + 30°) sin(A + B) = sinAcosB + cosAsinB sin(20°+30°) = (sin20°)(cos30°) + (cos20°)(sin30°) 0.76 = (0.34 x 0.87) + (0.94 x 0.5) 0.76 = 0.29+0.47 0.76 = 0.76 b) cos (30° + 40°) cos(A + B)...
  21. W

    Mastering Trigonometry: Graphing Sinusoidal Voltage with v = 6sin (314t + pi/2)

    A sinusoidal voltage is represented by the formula v = 6sin (314t + pi/2). Sketch the graph on the graph paper provided for values of t from 0.0s to 0.04s and show on the graph the values of • the amplitude • the time period and show how the frequency of the waveform may be determined from...
  22. Z

    Trigonometry Problem Solving Question

    Question: "A cat sitting on the edge of a straight river bank spots a bird sitting in a tree directly across the river's edge. The angle of elevation from the cat to the bird is 15°. The cat the moves 25m along the river bank, and now spots the same bird at an angle of elevation of 13°. How...
  23. Y

    Solving a Trigonometry Question: Understanding the Equation and Breaking it Down

    From the equation, it implies: \left[\frac{\cos\left(\frac{\pi}{2}\cos\theta\right)}{\sin\theta}\right]^2=\sin^3\theta For the life of me, I have no idea how this come about. I don't even know where to start, this implies ##\cos\left(\frac{\pi}{2}\cos\theta\right)=\sin^{\frac 5 2}\theta##...
  24. E

    Trigonometry Practice Problems: Finding Distances and Angles

    Homework Statement As per the attachment The Attempt at a Solution for a) sin58° = 32/hyp hyp*sin58°=32 hyp=32/sin58° hyp=32/0848 hyp=37.73 so to the nearest km between towns W & Y = 38km b)cosθ=adj/hyp cosθ=27/38 cosθ=0.710 θ=cos^-1(0.710) θ=44.76 so to the nearest...
  25. C

    Trigonometry Problem - Confused over multiple possible angle sizes.

    Homework Statement In triangle PQR, the length of QR is 4 mm, the length of PR is 3.5 mm and the size of angle Q is 60°. What are the possible size(s) of angle P (to 2 decimal places) The possible solutions are 138.81, 81.79, 118.96, 61.04, 98.21 The Attempt at a Solution I've solved for...
  26. Petrus

    MHB Solve the Trigonometry Equation: sin^-1(x) + cos^-1(2x) = π/6

    Hello MHB, I am working with an old exam Solve this equation \sin^{-1}(x)+\cos^{-1}(2x)=\frac{\pi}{6} progress: I start take cos both side and I get 2x+cos(\sin^{-1}(x))=\frac{\sqrt{3}}{2} I draw it and call the bottom side for B and get so we got \sqrt{1-x^2}+2x=\frac{\sqrt{3}}{2} Is this...
  27. N

    Trigonometry 3d pyramid question

    Homework Statement http://imgur.com/x8D2wqO I need to solve for theta and I keep getting the angle 65, using cosine law and pythagorean theorem but the answer key says that the angle is 93. The diagram is not to scale. Is my answer wrong or is the answer key incorrect?
  28. M

    Trigonometry Question: Find the Value of sin(α +2β) When cot (α + β) = 0

    Homework Statement If cot (α + β) = 0 then sin(α +2β) is the options are a. sin α b. cos α c. sin β d. cos 2β Homework Equations There is as such no equation The Attempt at a Solution I did try to solve it but I kept arriving at the wrong answer. The correct...
  29. S

    Trigonometry Limit Homework: Get Started Now!

    Homework Statement \lim_{x \to \frac{\pi}{3}} \frac{1-2 cos x}{\pi - 3x} Homework Equations trigonometry identity properties of limit for trigonometry The Attempt at a Solution I have done several attempts but got me nowhere. I just need an idea to start. Thanks
  30. S

    How Do You Solve This Trigonometric Limit Problem?

    Homework Statement \lim_{x \to 0} \frac{tan (cos 4x - 1)}{3x ~ sin (\frac{4}{3} x)} Homework Equations limit for trigonometry The Attempt at a Solution can I do it like this: \frac{tan (cos 4x - 1)}{3x ~ sin (\frac{4}{3} x)} = \frac{- tan (2 sin^{2} 2x)}{3x ~ sin (\frac{4}{3}...
  31. H

    TRIGONOMETRY equation derivation [HELP]

    The signal length from satellite to the Earth station (AC) can be found as 2(H)/[{sin^2(theta)+(2(H)/R)}^1/2+sin(theta)] Due to the Earth projection where "H" is satellite height and and R is the Earth radius My question is Can you help me to derive this equation? how they have...
  32. R

    Can you explain TRIGONOMETRY equation [HELP]

    The signal length from the satellite to the Earth station can be found as2(hs-he)/[{sin^2(theta)+(2(hs-he)/Re)}^1/2+sin(theta)] if theta < 5 degrees Due to the Earth projection where "hs" is satellite height and "he" is the Earth station height and Re is the Earth radius=3700 Km My question is...
  33. trollcast

    Trigonometry (Double angle formula)

    Homework Statement Calculate the value of \tan(\frac{\pi}{12}) without the use of a calculator and showing all steps. Homework Equations Compound angle formula / Double angle formula The Attempt at a Solution Using an equilateral triangle of side length 2 I've shown that...
  34. N

    MHB Trigonometry in mechanics

    Hi! I am finding the work-energy principle and idea of total mechanical energy hard to apply to finding the work done against/by a particular force. For example in the question below, why is there no work done against the weight of the skier acting down the slope? Any help would be great! Thanks :D
  35. Vahsek

    Finite sum formula for tangent (trigonometry)

    Hi everyone, I've been looking for the finite sum formulae of trig functions. I've found the easiest ones (sine and cosine). But the one for the tangent seems to be very hard. No mathematical tricks work. Plus I've looked it up on the internet. Nothing. I will greatly appreciate your help...
  36. A

    How can I solve this Trigonometry equation in RxR?

    Homework Statement we have sin(3x)=cos(2y) sin(x+pi/3)=cos(y-pi/3) solve in RxR Homework Equations The Attempt at a Solution i tried squaring both sides and turning everything to cos 2a then turning it into an XY=0 but that didn't help at all i ended up with y=0 which...
  37. K

    Trigonometry Substitution (Integral)

    Homework Statement ∫xtan^-1(x^2)dx Homework Equations The Attempt at a Solution I did u = x, du = 1, v = ? ,dv = tan^-1(x^2)dx I do not know how to get the integral of tan^-1(x^2)
  38. K

    Trigonometry Substitution (Integral)

    Homework Statement Making sure I got the right answer.Homework Equations The Attempt at a Solution
  39. I

    Trigonometry identity sin(pi)cos(wpi)+cos(pi)sin(wpi)

    Homework Statement Hi guys, How can sin(∏)cos(ω∏)-cos(∏)sin(ω∏) = sin(ω∏)? please guide me trigonometry identity to apply with this? Homework Equations The Attempt at a Solution
  40. C

    MHB Using Trigonometry for solving a Cubic equation

    Dear Everyone, I need some help for this general cubic equation. \[ax^3+bx^2+cx+d=0\]. First divide the equation by a \[x^3+b/ax^2+c/ax+d/a=0\] Let x=y-b/(3a) ... $$y^3+py+q=0$$ where $$p=c/a-(b/a)^2)/3;q=d/a-(b/a*c/a)/3+(b/a)^3/27$$ $$y=cos \theta$$ then i need to use the identity for...
  41. E

    Trigonometry study on the side

    I'm about to take a trig class and it's been a while since my last math class. I was wondering if you guys knew of any websites that have good trig study guides and study sheets? anything is appreciated! Thanks!
  42. U

    Inverse trigonometry prove this

    Homework Statement If cos^{-1}\frac{x}{a}+cos^{-1}\frac{y}{b} = \alpha then show that \frac{x^2}{a^2}-\frac{2xy}{ab}cos \alpha + \frac{y^2}{b^2} = sin^2 \alpha Homework Equations The Attempt at a Solution I assume inverse functions to be θ and β respectively. So in the second equation...
  43. I

    Basic Trigonometry: Explaining the Rules

    We all know that sin theta = opposite side / hypotenuse cos theta = adjacent side / hypotenuse tan theta = opposite side / adjacent side. But why? Are there some explanations behind or are they just defined by scientists?
  44. B

    Schools Is taking trigonometry and college algebra at the same time a bad idea?

    My professor is advising me against this. Also my friend who is an ME is advising against this as well. I am not sure why. I enjoy math and grasp the concepts pretty fast. A little history, I was a nursing major, but soon realized I wanted more than that. I was then torn between becoming a...
  45. X

    Right angle trigonometry homework question

    Homework Statement A steel plate has the form of one-fourth of a circle with a radius of 60 centimeters. Two two-centimeter holes are to be drilled in the plate positioned as shown in the figure. Find the coordinates of the center of each hole.Homework Equations I know it's got to be a simple...
  46. 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...
  47. 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...
  48. 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...
  49. 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...
  50. 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
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