What is Trigonometery: Definition and 84 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

    Why Is Sin(theta) Squared in This Mechanical Engineering Problem?

    Hi! New to this forum and signed up because I've just started a foundation degree in mechanical engineering, and having been out of education for a very long time beforehand, getting back to grips with mathematics and the like! Anyway, I would like to ask for some advice on this problem, I know...
  2. F

    Foundations I have complied a list of textbooks about Trig, Algebra, Etc

    I am planning to self-teach myself Trigonometry and all the other required fields before jumping into calculus. I have compiled a list of books that I have researched and would like your opinions and recommendations. Books: Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry...
  3. D

    Solve acos²θ+bsinθ+c=0 for all values 0≤θ≤360°

    Homework Statement Solve acos²θ+bsinθ+c=0 for all values 0≤θ≤360° a=16 b=6 c=-12 So 16cos²θ+6sinθ-12=0 Homework Equations Cos²x=1-Sin²x The Attempt at a Solution Identity: Cos²x=1-Sin²x 16(1-Sin²θ)+6Sinθ-12=0 16-16Sin²θ+6Sinθ-12=0 6Sinθ-16Sin²θ=12-16=-4 Divide by 2(?) 3Sinθ-8Sin²θ=-2...
  4. dfklajsdfald

    Finding the Value of axb on the Unit Circle | Round to the Nearest Thousandths

    Homework Statement the point (log a, log b) exists on the unit circle. find the value of axb. round to the nearest thousandths. Homework Equations x2 + y2 = 1 The Attempt at a Solution x2+y2 = 1 loga2+logb2 =1 2loga+2logb = 1 2(loga+logb) = 1 loga + log b = 0.5 logb = 0.5−loga now i try...
  5. S

    B  Given circle, find the line of bearing of tan lines thru 0,0

    This question occurred to me a few days ago and it's been bugging me ever since. Consider a circle in the coordinate plane with center P(x,y) and radius R, where R < D, D being the distance from the origin to the circle's center. There are two lines tangent to the circle (T1 and T2) that pass...
  6. Liam C

    B What do Sine, Cosine and Tangent do?

    When I press these buttons on my calculator to find the third side or an angle in a triangle, what calculation is happening? What is the logic behind it all? I know it's a very basic question, but I am only in grade 10 and have not started Math yet this year.
  7. Jonski

    Velocity of a slider connect to a wheel

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  8. Alettix

    Trigonometric Equation Solving: Cosine and Sine Identities for Homework

    Homework Statement The following equation is to be solved for all x: ## \cos(x) + \cos(3x) = \sin(x) + \sin(3x)## Homework Equations The tripple angle formulas: ## \cos(3x) = 4\cos^3(x) - 3\cos(x) ## ##\sin(3x) = 3\sin(x) - 4\sin^3(x) ## The Pythagorean trig identity: ## \sin^2(x) + \cos^2(x)...
  9. Rectifier

    Trigonometry - Solving Trigonometric Equations

    The problem I am trying to write ##-sin 2x + \sqrt{3} \cos 2x ## as ## A \sin(2x+\phi)## without using this formula below ##a sin (x) + b cos (x) = c sin (x+v), \ \ c=\sqrt{a^2+b^2} \ ,\ \ \tan v = \frac{b}{a}## The attempt ##A \sin(2x+\phi) = A \cos(\phi) \sin(2x) + A \sin(\phi)...
  10. P

    B Smallest number whose sin(x) in radian and degrees is equal?

    Question: what is the smallest positive real number x with the property that the sine of x degrees is equal to the sine of x radian? My try: 0. But zero isn't a positive number. How do I even begin to solve it? I tried taking inverse on both sides of sin(theta)=sin(x), but that didn't help.
  11. P

    B How to find out various sine values from its graph.

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  12. Liam C

    Solve Trig Problem: Horizontal Dist. Between Truck & Dock to Nearest Tenth

    Homework Statement A loading ramp is 2.8m long. One end rests on a loading dock 0.7 meters above the ground, and the other end leads into the back of a a tractor trailer 1.2m above the ground. Find the horizontal distance between the back of the truck and the loading dock, to the nearest tenth...
  13. T

    Solution Set for cot-1(x)2 -(5 cot-1(x)) +6 >0?

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  14. T

    What is the solution to the inverse trigonometry problem with a given range?

    Homework Statement If 1/2<=x<=1 , then cos-1[ x/2 + (√(3-3x2))/2] + cos-1 x is equal to? Homework EquationsThe Attempt at a Solution Substituting x=cosθ = cos-1(cosθ) + cos-1 [ cos(θ)/2 + (√(3(1-cos2(θ)))/2] = θ + cos-1 [cos (π/3) cos θ + sin (π/3) sinθ] =...
  15. 1

    Why is this triangle not right? (sine -1 is bigger than 1)

    the black triangle is given, and red triangle is me trying to work it out why is my trangle wrong? and what is the right triangle? someone is sliding down a slope, with 2ms-2 of acceleration (not actually given which direction, maybe I'm wrong there, but the person is acelerating at 2ms-2 down...
  16. P

    B Are there multiple ways to verify a trig identity?

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  17. P

    Finding sum of roots of trigonometric equation

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  18. P

    Calculate initial speed of an athlete - projectile motion

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  19. Elvis 123456789

    How to go from a*cosx + b*sinx TO A*cos(wt - phi)?

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  20. F

    How Can I Correctly Integrate e^(ix)cos(x)?

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  21. C

    Trig Identities: Simplifying Expressions with Cotangent, Secant, and Cosecant

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  22. E

    Solving -25FCosα + 1.5FSinα= -80 with Trigonometric Identities

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  23. F

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    Ok, I have encountered this one a few hours ago: \int \frac{cos x}{\sqrt{a - b cos x}}dx I have tried all techniques I know, integration by part, half-angle formula, substitution, trigo approach, and so on, but it seems, I could not integrate this one. I am no noob in integration, but this one...
  24. Dean Whaley

    Solve for a constant in an equation

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  25. J

    Answer "Solving 2D Elastic Collision Homework

    Homework Statement A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball. If the first ball moves away with angle 30° to the original path, determine: a. the speed of the first ball after the collision. b. the speed and direction of the second ball after...
  26. patrickbotros

    A Find the minimum without Calculus or Graphing

    ƒ(ß)=.5sec(ß) + √[1+(sec2(ß)/4)+tan(ß)/√(2)] Without graphing it or using calculus find the minimum. I already know the answer but want to know how to do it. It s at π/12 and is something like 1.5. First off this is NOT a homework problem. I already know the answer is something like 1.5 at π/12...
  27. DaniV

    The Trigonometery functions in other presentation

    Can I present the trigonometry functions (such as SinX, CosX, TanX, CotX) by using only- Log, Lan, multiplication, division, addition, subtraction, exponantion, nth root operations?
  28. S

    Elastic collision in 2-dimensions

    Homework Statement A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball. If the first ball moves away with angle 30° to the original path, determine: a. the speed of the first ball after the collision. b. the speed and direction of the second ball after...
  29. Chrono G. Xay

    'Wheel-like' Mathematics (Modulating Trig Functions?)

    As part of a personal musicology project I found myself with the mathematical model of a geometry which utilizes the equation a*(a/b)sin(pi*x) The only problem with this is that I need to take the integral from -1/2 <= x <= 1/2, and according to Wolfram Alpha no such integral exists. I can...
  30. TBan

    Use of Gyro/Accelerometer for Boat Tilt Application?

    Hello, I'm looking to try to use a gyroscope to determine the rocking motion (just side to side - not back and forth) of a boat while it is traveling forward or sitting still in the water. Specifically, I'm looking for the boat's angle from vertical and this angle's velocity. Can I do this...
  31. Camperwes

    Should I Take Pre-Calculus Before Entering Calculus?

    So I have been out of Math Courses for 5 years then this semester Spring Semester I completed Pre Algebra with an A, this Summer I have two Semesters of which I am taking College Algebra for Science and Engineering Majors and Plane Trigonometry. My question is during the Fall Semester should I...
  32. J

    Why Does My Integral Calculation Differ from the Expected Result?

    The result of the integral of (1/2)sin2x dx with: upper limit x = arccos((R-h)/R) lower limit x = 0 is (-h^2+2Rh)/(2R^2) I can not seem to get this exact answer my workings yield: let u = 2x, du/dx = 2 therefore dx = du/2 Integral becomes (1/4) ∫ sinu du (with the same upper and lower...
  33. S

    What are the forces acting on a sliding box?

    I was asked to draw a free body diagram to derive the equation tan θ = µs for the following situation: A box sliding down an inclined plane. My FBD has 3 forces - gravitational forces pointing downward (horizontally) <-- longest vector - normal force perpendicular to the box - frictional...
  34. ichabodgrant

    Prove arcsin x for its logarithm form

    Homework Statement Given sin x = (eix - e-ix) / 2i, I want to prove that arcsin x = -i ln(ix + √1 - x2) Homework Equations I know about the Euler's formula and complex number. But I have never learned about complex logarithms. The Attempt at a Solution I try to use x = sin y. But it seems...
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