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. CK_KoopaTroopa

    I Finding the max angle of a longboard deck before the wheels slip

    Hi, I'm making an electric longboard and trying to write an app for my phone to function as the remote. I've got a bunch of fancy Star-Trek-esque indicators on it, one of which is the pitch and roll of the deck. All the indicators have "danger zones" and turn red when they hit them, and for this...
  2. snoopies622

    Are desert ants capable of trigonometry for navigation?

    Was just reading in Clifford A. Pickover's "The Math Book" that ants of the Sahara desert can, after wandering in a non-linear path to find food, from there go directly back home without a line of sight between the two locations. I don't see how one can arrive at the correct direction and...
  3. JTC

    I Why does the cross product operation adhere to the right-hand rule?

    (First, I am aware there is no cross product in higher dimensions. I am aware of differential forms. I am aware of the problems with the cross product. I know enough to know what I don't know. but set all that aside.) With that, could someone help me, by properly phrasing the cross product...
  4. H

    What is the Sum of Angles a and b in This Trigonometry Problem?

    Homework Statement ##\sin a + \cos b## = ##\frac{-1}{2}## ##\cos a + \sin b## = ##\frac{\sqrt 3}{2}## 0 < a < ##\pi/2## ##\pi/2## < b < ##\pi## a + b = ? By calculating sin (a+b) Homework EquationsThe Attempt at a Solution I tried : ##\sin a + \cos b = 2sin\frac{(a+b)}{2}cos\frac{(a-b)}{2}...
  5. opus

    Trigonometry- Converting from DMS to DD and rounding

    Homework Statement Convert 24*8'15'' to Degree Decimal notation. Round to the nearest second. (Let * denote the 'degree' symbol. I couldn't find it anywhere in Latex) Homework EquationsThe Attempt at a Solution 24* + 8[(1)/(60)]* + 15[(1)/(3600)]* = 24.1375* This is the solution, before...
  6. blixel

    Trigonometry: Another Statics Problem

    Homework Statement A subdivision lot is 200 ft long by 80 ft wide. A surveying crew made an error of 0.10 degrees when setting the iron pin in the corner of the lot shown. By what distance is the correct pin off of the true corner? Homework Equations I think I'm doing this one right...
  7. blixel

    Trigonometry: Wanting someone to check my answer for Statics

    Homework Statement A building is 400 ft tall and has suffered damage from a recent earthquake. If a surveyor is stationed 150 ft away, sets a zero angle on the bottom corner of the building, and turns the angle shown to the top of the building; what is the angle at which the building is leaning...
  8. Curiose

    So, is my approach for finding angles efficient and accurate?

    For one of my current projects in computer vision (which really is a study in point clustering and tracking in a data stream of n-dimensional data), I have come up with a way to very quickly index a 2D angle between two points or the angle of a vector. Doing a little bit of investigation, and...
  9. Wrichik Basu

    Intro Math Books on Spherical Trigonometry

    What are some good books to learn spherical trigonometry from basics to the advanced level?
  10. MrGoATi

    Trigonometry: count sin+cos when tg-ctg=-7/12

    Mentor note: Moved thread to homework section ok So I'm doing supposedly easy trigonometry problems. i did the easiest ones. now I have no idea how to solve 2. first one is count sin+cos When tg - (1/tg) = -(7/12) what i figured is that i probably need to use...
  11. L

    I Exploring the Limits of Trigonometry: 0 < sin x < x

    Given that 0 < sin x < x is true for 0 < x < π/2. From the above, can we conclude that 0 < sin (x/2) < x/2? How about 0 < sin (x/5) < x/5? Why? How about 0<sin 3x < 3x ? Why?
  12. D

    Elastic collision - Trigonometry equations

    Homework Statement A billiard ball moves at a speed of 4.00m/s and collides elastically with an identical stationary ball. As a result, the stationary ball flies away at a speed of 1.69m/s, as shown in Figure A2.12. Determine: the final speed and direction of the incoming ball after the...
  13. J

    Geometry: Solve for angles of a triangle w/line intersecting

    My mother's boyfriend's son who is in 6th grade asked me a question about the math they are learning. I thought it wouldn't be too bad but I cannot for the life of me figure it out. A solution would be greatly appreciated. 1. Homework Statement https://postimg.org/image/1tsa4v4t8r/ Homework...
  14. A

    B Trigonometry Identity Question

    Can someone please tell me how sin(180 - x) = sin x? Here my attempt: sin (180 - x) = sin 180 . cos x - cos 180 . sin x Next? I have no idea...
  15. H

    How to prove this trigonometry equation?

    Homework Statement I opened my old math book and interested in this Proof Cos (A-B) - tan(A-D) = (2cos A)/(sin 2A + sin 2B) Homework Equations Cos(A-B) = cosA cosB + sinA sinB Tan(A-D) = (Tan A - tan B)/(1+Tan A Tan B) The Attempt at a Solution cosA cosB + sinA sinB - (tan A - tan B)/(1+Tan...
  16. W

    MHB Some Geometry Some Calculus Some Trigonometry

    Show that y≈∆φ×secφ in the jpeg attached. or ∆y = sec φ A and B are points on curved surface, two lines are extended through origin to a line that is tangent to the circle, these points are A' and B', change in Angle will bring a change in length between A' and B'. I need to know how is this...
  17. M

    MHB Trigonometry and periodic functions

    !HELP! The Singapore Flyer, until recently the world's largest Ferris wheel, completes one rotation every 32 minutes.1 Measuring 150 m in diameter, the Flyer is set atop a terminal building, with a total height of 165 m from the ground to the top of the wheel. When viewed from Marina Centre, it...
  18. P

    MHB Violet's Trigonometry Questions via Facebook

    1. By applying the sine rule we have $\displaystyle \begin{align*} \frac{\sin{ \left( A \right) }}{a} &= \frac{\sin{ \left( B \right) } }{b} \\ \frac{\sin{ \left( \alpha \right) }}{10} &= \frac{\sin{ \left( \beta \right) }}{8} \\ \frac{\frac{2}{3}}{10} &= \frac{\sin{ \left( \beta \right) }}{8}...
  19. P

    Algebra What is a great book for completing Algebra and trigonometry?

    Once I complete high school geometry, I am planning to take algebra 2 and trigonometry next. I am asking if there are good textbooks out there that provide a full course of algebra 2 and trigonometry. Or should I take these two courses separately? By the way, I am self-studying.
  20. H

    Find theta given known cos and sin....

    Homework Statement Homework Equations cos 2theta = costheta^2 - sintheta^2 The Attempt at a Solution cos2theta = 1 2theta = 0, 2phi but i get wrong answer.. how is it?
  21. M

    I Using trigonometry to create a radar for a game.

    I am making a video game using Game Maker Studio 2.0 and am making a radar. To give you some background, one object is obj_Player, and the other is obj_Sub. The radar gives the sub's position and distance from the player (center of radar). The first part of my radar works perfect. I normalized...
  22. Vital

    Is there an algorithms to determine correct angles

    Homework Statement Hello! I am struggling with plotting polar graphs manually (without any help of the calculator). My main unresolved issue is with finding correct values of theta in a given range. For example, I have an equation: $r = cos(5\theta)$ Homework Equations and I know that the...
  23. Wrichik Basu

    A problem in Inverse Circular Functions in Trigonometry

    Homework Statement :[/B] Solve for ##x ##: $$ \sin ^{-1} {x} +\sin ^{-1} {(1-x)} =\cos ^{-1} {x} $$ Answer given: ##0## or ##\frac {1}{2}##. Homework Equations :[/B] All relevant formulae on inverse circular functions may be used. The Attempt at a Solution :[/B] Please see the pic below...
  24. Wrichik Basu

    A problem in Trigonometry (Properties of Triangles) v3

    Homework Statement In any triangle ABC, prove that $$a^2 b^2 c^2 \left (\sin {2A} +\sin {2B} + \sin {2C} \right) = 32 \Delta ^3$$ Here ##\Delta ## means the area of the triangle.Homework Equations The Attempt at a Solution
  25. Wrichik Basu

    A problem in Trigonometry (Properties of Triangles) v2

    Homework Statement In any triangle ABC, prove that $$ a^2 + b^2 +c^2 =4 \Delta (\cot {A}+\cot {B}+\cot {C}) $$ Homework Equations The Attempt at a Solution
  26. Wrichik Basu

    A problem in Trigonometry (Properties of Triangles)

    In any triangle ABC, prove that $$(b+c-a) \left( \cot {\frac {B}{2}} + \cot {\frac {C}{2}} \right)=2a \cot {\frac {A}{2}} $$
  27. donaldparida

    B What are some strategies to prove trigonometric results

    I am facing a lot of problem in proving trigonometric results (advanced ones). There are a lot of formulas (compound angle related ones, transformation of sum into product ones and vice versa, multiple angle and sub-multiple angle ones). I am unable to figure out how to proceed forward in...
  28. Bunny-chan

    Determining a trigonometric limit

    Homework Statement Calculate the following limit: Homework EquationsThe Attempt at a Solution I don't know how to proceed with this. I've tried to multiply by the conjugate, and to simplify the expression (x+\pi) to u, but I wasn't very sucessful. To what kind of algebric device I could...
  29. Bunny-chan

    Book demonstration about trigonometric relations

    Homework Statement [/B] In the equation between (3) and (2), why does the author says that ? Isn't the trigonometric identity actually ? 2. Homework Equations The Attempt at a Solution
  30. D

    MHB Can you find x using the trigonometry of circle sectors?

    I need help in solving this problem. Below shows all the measurements of the diagram, I need to find x:
  31. Bunny-chan

    Basic trigonometry in dynamics force problem

    Homework Statement Two spheres, with 0.5g each, are hanging by 30cm threads, tied on the same spot. The same electric charge is communicated to each sphere; in consequence, the threads move apart until they are about 60^\circ from each other. What is the value of the charge? \theta =...
  32. awholenumber

    B Some questions about trigonometry

    Does these two picture cover everything about trigonometry ? Is anything important missing ?
  33. D

    [Calc] First max and min values of an underdamped oscillation

    Homework Statement Determine the FIRST maximum and minimum values of the underdamped oscillation: y=e^(-x/2)(4sin(3x)+3cos(3x)) cm Homework Equations 3. The Attempt at a Solution [/B] I firstly differentiated the above equation and got: (-e^(-x/2)(22sin(3x)-21cos(3x)))/2 I checked this and...
  34. Epsilon645

    Finding the Height of a Circular Roller in a Symmetric Worm Thread

    Homework Statement The machine tool diagram on the right shows a symmetric worm thread, in which a circular roller of diameter 1.5 inches sits. Find the amount d that the top of the roller rises above the top of the thread, given the information in the diagram. (Hint: Extend the slanted sides...
  35. K

    B Average angle made by a curve with the ##x-axis##

    The average angle made by a curve ##f(x)## between ##x=a## and ##x=b## is: $$\alpha=\frac{\int_a^b\tan^{-1}{(f'(x))}}{b-a}$$ I don't think there should be any questions on that. Since ##f'(x)## is the value of ##\tan{\theta}## at every point, so ##tan^{-1}{(f'(x))}##, should be the angle made by...
  36. C

    I have no clue what to do with Trigonometry

    I have been failing some tests on trig and one question was sinx=cos48. I have no clue what it means, please help
  37. K

    I How do I evaluate the Taylor series for ##Si(x)## around a given value?

    Hi, I've got this: $$\sin{(A*B)}\approx \frac{Si(B^2)-Si(A^2)}{2(\ln{B}-ln{A})}$$, whenever the RHS is defined and B is close to A ( I don't know how close). Here ##Si(x)## is the integral of ##\frac{\sin{x}}{x}## But, to check it, I need to evaluate the ##Si(x)## function. I'm new with Taylor...
  38. D

    I Trigonometry problem for collision detection and reflection

    A particle moves from point 0 to point 2. Both positions are known. The center of the circle and it's radius is also known. I am trying to work out the position of 1 where the particle strikes the circle. This is for a 2D astronomy simulator to work out where a particle will strike a 2D...
  39. Kaura

    Solve for Path of Particle: x - 2cos(arcsin(y/2)) = 0

    Homework Statement Suppose that a particle follows the path r(t) = 2cos(t)i + 2sin(t)j Give an equation (in the form of a formula involving x and y set equal to 0 ) whose whose solutions consist of the path of the particle. Homework Equations None that come to mind The Attempt at a Solution I...
  40. chwala

    What Steps Can Resolve a Trigonometric Equation Involving Sine and Cosine?

    Homework Statement [/B] Solve ##2sin3x.sinx=1##Homework EquationsThe Attempt at a Solution I used the identity ##( cos (A+B)= cos A cos B- sin A sin B), (cos(A-B) = cos A cos B+sinA sinB)→ -(cos 4x-cos2x)= 2sin 3xsinx, (cos 2x-cos4x=1)##now i am stuck , is this correct_ using ##(cos...
  41. parshyaa

    B Exploring the Applications of Trigonometric Functions Beyond 90°

    Why trigonometric functions are defined for unit circle, here "why" refers to what made them to define it this way, they may have defined it for right triangle only , can you give me a application where sin(120°) or sin, cos , tan of more than 90° is used to find some values like in physics or...
  42. S

    Courses How much trigonometry is used in high level math?

    Hi all. I'm a liberal arts graduate looking to enter a statistics masters program (in case it matters). I'm retaking some lower level courses to prove I can do math I wanted to know how much trig is used in Calc II and beyond. I didn't do great in that class (I'm going to retake it) and when I...
  43. Albert1

    MHB Using trigonometry to prove <c=50 degree

    $\triangle ABC,\angle B=30^o$ and $\overline{BC}^2-\overline{AB}^2=\overline{AB}\times \overline{AC}$ using trigonometry to prove $\angle C=50^o$
  44. parshyaa

    I Exploring Spherical Trig: Applications in Physics

    When do we learn about spherical trigonometry and what are its application(mostly in physics) I have read a formula named versed sine = 1- cos(θ) in the trigonometry book by S.L loney, I tried it on google to know more about it and the research made me shocked, haversine(half of versed sine)...
  45. Clara Chung

    How Can the Maclaurin Series Validate a Trigonometric Inequality?

    Homework Statement show that 1-t^2/2 <=cos(t) <=1 for 0<=t<=1 Homework Equations Trigonometry knowledge The Attempt at a Solution I don't know how to relate t with cos(t), and I also try to find out cos(1), but there is no result, so how can I start with this problem.
  46. terryds

    Solving Trigonometry Problems: How to Find CE Using the Cosine Rule

    Homework Statement I don't understand how to get CE. Homework Equations Trigonometric identities (maybe) The Attempt at a Solution [/B] First, I start with the cosine rule CB^2 = AC^2 + AB^2 - 2 AC AB cos α (CE/sin(β))^2 = (CE/sin(α))^2 + L^2 - 2 (CE/sin(α)) L cos α which is going to be...
  47. I

    High School Level Physics Homework

    Homework Statement A highway is to be built between two towns, one of which lies 35.0km south and 72.0km west of the other. What is the shortest length of highway that can be built between the two towns, and at what angle would this highway be directed with respect to due west. Homework...
  48. pairofstrings

    Visualize this type of Combined Trigonometric Functions

    Homework Statement Show that sin 600° . cos 330° + cos 120° . sin 150° = - 1 Homework Equations I know that sinΘ = opposite/hypotenuse and cosΘ = adjacent/hypotenuse. The Attempt at a Solution I am equipped with knowledge about what sinΘ and cosΘ is from right angled triangle. I stand in...
  49. M

    Studying Need someone to tell me the topics to practise to study trigonometry

    I across a video about how to be good enough at anything within 20 hours. It said that first to get rid of all barriers and the identify The small skills which are used in the thing you're trying to "become good enough at ",in this case in solving trigonometry questions, and grind them...
  50. Rectifier

    Show that ##\sin(\arctan x) < x < \tan(\arcsin x)##

    The problem For ##0 < x < 1 ## . Show that $$ \sin(\arctan x) < x < \tan(\arcsin x) $$ The attempt I know that ## \sin x < x < \tan x ## is true for ## 0 < x < \ \pi / 2 ## x - is by definition the length DA (in radians) I draw a right triangle with sides x and 1 and with hypotenuse ##...
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