What is Trigonometry: Definition and 660 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. 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...
  2. 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...
  3. 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...
  4. 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## ??
  5. 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...
  6. C

    Hockey Rink Optimization problem

    Homework Statement [/B] Solve optimization problem; A person is to skate up a hockey rink, in a straight line(parallel to both of the sides), from wherever they are standing. They are to shoot the puck into the net whenever they reach the point where the angle on the net is the largest. Need to...
  7. N

    Please recommend me a good math book prior to taking trigonometry

    Hello, I asked for help on the "Science & Math Textbooks" subforum, but it looks like there are not many users in there. So I hope you don't mind if I ask for help in this subforum since I need help on this soon. Copy and paste from my other thread: "Hello, it has been a few years since I took...
  8. K

    Intensity of polarized light that has passed through two polarizing sheets

    Homework Statement A beam of polarized light of intensity 43.0 W/m2 is sent through a system of two polarizing sheets. Relative to the polarization direction of that incident light, the polarizing directions of the sheets are at angles θ for the first sheet and 90 degrees for the second...
  9. N

    Geometry Please recommend me a good math book prior to taking trigonometry

    Hello, it has been a few years since I took an algebra class, and therefore I have already forgotten a lot of material. I will be taking a college trigonometry class soon during winter session and I was wondering if you could recommend me a good Algebra I and II book to review before taking the...
  10. Y

    Trigonometric Identity for Solving Sin Cubed Equations

    Homework Statement sin ^{3}x + sin ^{3}(\frac{2\pi}{3} + x ) + sin ^{3}(\frac{4\pi}{3} + x) = \frac{-3sin3x}{4}Homework Equations sin 3x = 3sin 3x - 4sin^{3}x Mod note: The correct identity is ##sin(3x) = 3sin(x) - 4sin^3(x)## The OP realized this earlier but was unable to edit his/her post.The...
  11. deusy

    Determining the Period of sin(ax)*cos(bx)

    Homework Statement I'm trying to work out the period of a function of the form sin(ax)*cos(bx), where a =/= b. I'm trying solve how the values for a and b relate to the period. I've graphed a lot of functions, but I'm struggling to notice any patterns. The period always seems somewhat related...
  12. C

    Understanding Vector Calculus & Trigonometry for Physics

    Hi. Every time i read physics I feel so discouraged by my lack of understanding in terms of vector calculus and trigonometry. I do understand basic trigonometry and basic vectors but when professors or textbooks move onto combining derivatives with vectors i lack understanding of which rules...
  13. L

    Complex numbers in trigonometry form

    Homework Statement Write down number 1+i and 1+i\sqrt{3} in trigonometry form.[/B]Homework Equations For complex number z=x+iy \rho=|z|=\sqrt{x^2+y^2} \varphi=arctg\frac{y}{x} And [/B]The Attempt at a Solution Ok. For z=1+i \rho=\sqrt{1+1}=\sqrt{2}...
  14. P

    Is there an equivalent of cosx=1-(x^2/2) for the sin function

    Hi, i was just wondering since cosx=1-(x^2/2) is there a similar formatted formula for sinx?? much appreciated :) :)
  15. Summer95

    Force Components, Friction, etc. Check my work?

    Could someone credible please check my work on this one? Homework Statement This problem is "pulling a sled up a slope" All relevant data is in the picture. I wanted to find FP (The force one has to pull to start the sled moving up with slope). mass = 26.0kg μs = 0.096 slope of hill = 12...
  16. S

    Trigonometric Limit without L'Hôpital's Rule

    Homework Statement "Calculate the following limit if it exists. If it does not exist, motivate why. \displaystyle\lim_{x\rightarrow 0} {\frac{x + x^2 +\sin(3x)}{tan(2x) + 3x}} Do not use l'Hôpital's rule." Homework Equations (1) \sin(a\pm b) = \cos(a)\sin(b)\pm\cos(b)\sin(a) (2)...
  17. N

    Why does [sin(θ/2)-cos(θ/2)]^2 not always equal 1?

    Homework Statement Does [sin(θ/2)-cos(θ/2)]^2 equal 1 for all values of θ? I need to figure this out to solve a physics problem. Homework Equations sin^2(A)+cos^2(A)=1 The Attempt at a Solution [sin(θ/2)-cos(θ/2)]^2 =sin^2(θ/2)+cos^2(θ/2) =1 But this isn't what I get when I put...
  18. anemone

    MHB How Do You Solve This Trigonometry Challenge Involving Cosine Powers?

    Evaluate $2\cos^3 \dfrac{\pi}{7}-\cos^2 \dfrac{\pi}{7}-\cos \dfrac{\pi}{7}$.
  19. kaliprasad

    MHB Proof: $\tan\,6^{\circ}\tan\,42^{\circ}\tan\,66^{\circ}\tan\78^{\circ}=1$

    prove that $\tan\,6^{\circ}\tan\,42^{\circ}\tan\,66^{\circ}\tan\,78^{\circ} = 1$
  20. anemone

    MHB Is $\sin^2 x$ Less Than $\sin x^2$ for $0 \leq x \leq \sqrt{\frac{\pi}{2}}$?

    Hi MHB, When I first saw the problem (Prove that $\sin^2 x<\sin x^2$ for $0\le x\le \sqrt{\dfrac{\pi}{2}}$), I could tell that is one very good problem, but, a good problem usually indicates it is also a very difficult problem and after a few trials using calculus + trigonometry method, I...
  21. anemone

    MHB Trigonometry Challenge: Can You Solve This Equation?

    Solve the equation $\sin^7 x+\dfrac{1}{\sin^3 x}=\cos^7 x+\dfrac{1}{\cos^3 x}$.
  22. P

    Solving a trigonometry equation simultaneously in two variables

    Homework Statement Solve the equations sin(x+2y)=1/2 , cos(2x-y)=1/ sqrt(2) Homework Equations The Attempt at a Solution I tried getting a generic solution for both the first and second equation. How do I further proceed? By simultaneously solving? I so, how? 2x-y=2m*pi + or...
  23. anemone

    MHB Trigonometry Challenge II: Solving for $m,\,n$ and $A$

    Find $m,\,n$ and $A$ such that $\sqrt{9-8\cos 40^{\circ}}=m+n\cos A^{\circ}$ where $m,\,n\in N$.
  24. A

    MHB Linear Approximation With Trigonometry

    Hey guys, I have just a few more questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. I'm only asking about 1ab, ignore 2abc please: So for the first one, I used cos(30) as the estimated value to approximate L(28). Then I...
  25. A

    MHB Derivatives and Inverse Trigonometry

    Hey guys, I have a couple of questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: For 1a, using inverse trigonometric derivative identities should work, right? I got y' = 1/sinØ + 1/cosØ and multiplied by the common...
  26. Glype11

    Troubleshooting Trigonometry: Finding Coefficient of Friction on a Slope

    This problem deals with finding the coefficient of friction between an object and a slope. It gives an object with mass m, sliding down a hill with a slope of θ at a constant velocity. I got mgsinθ=fksinθ. However the book shows mgsinθ=fk. The kinetic friction force and the force down the slope...
  27. anemone

    MHB Solve Trig Challenge: Find All Values of x

    Find all values of $x$ which satisfy $\tan \left( x+\dfrac{\pi}{18}\right)\tan \left( x+\dfrac{\pi}{9}\right)\tan \left( x+\dfrac{\pi}{6}\right)=\tan x$.
  28. D

    MHB Solve Trigonometry Angles: Degrees, Minutes & Seconds

    please help me to solve these problems, 1. how many degrees, minutes, and seconds are respectively passed over in $11\frac{1}{9}$ minutes by the hour and minute hands of a watch? 2. The number of degrees in one acute angle of a right-angled triangle is equal to the number of grades in the...
  29. T

    What is the use of spherical trigonometry and the pre recs to learn it

    What is the use of spherical trigonometry besides in navigation. My math background consist of having n completed a course in calculus 1. Would I ever need to learn and understand spherical trigonometry for further math or physics? What do I gain learning it besides saying I know spherical...
  30. GeorgeDirac

    Elementary Trigonometry problem

    My problem is from Israel Gelfand's Trigonometry textbook. Page 9. Exercise 7: Two points, A and B, are given in the plane. Describe the set of points X such that AX^2+BX^2=AB^2. The attempt at a solution Since problem asked to describe set of points X such that AX^2+BX^2=AB^2, I tried to...
  31. anemone

    MHB Geometry and Trigonometry Challenge

    A rectangle with sides $x$ and $y$ is circumscribed by another rectangle of area $A^2$. Find all possible values of $A$ in terms of $x$ and $y$.
  32. L

    What is the angle needed to see a distant point on a circle with a given radius?

    Homework Statement A circle with a radius (r) of 6000km. From the centre of the circle to a point in the distance G where another person is standing is R = 40000 km. Calculate the angle (θ) that the observer has to stand at point (O), to allow the observer to see the distant point G. If the...
  33. J

    What is the Trigonometry Behind Finding x in Two Triangles?

    Hi Guys, This is my second post relating to my problem, But I've boiled it down to more simple trig. sadly, I still can't figure it out. See the sketch below; what I want to obtain is x as a function of R. the angle in red, θ is the same for the two corners. What is known: 1) two...
  34. G

    Sheldon Axler's "Algebra & Trigonometry" vs. "Precalculus: A Prelude."

    Hi all, I've been looking and searching around for a good book for some pre-calculus review, and decided on one of Sheldon Axler's books. Looking at his site and the contents of both books (links below), I'm not sure what the difference is between them, other than some re-ordering of things...
  35. C

    Self-study Alegbra, PHysics and trigonometry books?

    Hi awesome people at physicsforum, I’m planning on doing some self-study in physics and math and I’d really appreciate some advice based on my skill -level and what I want to achieve, which I’ll describe for you. I’ve considered some books to buy further down, and would deeply appreciate...
  36. johann1301

    How Does COS Ø = 0.99 Affect Transformer Efficiency?

    On a trafo i just bought, it says COS Ø = 0,99. What does this mean? Is there some angle involved in changing the voltage?
  37. K

    MHB Trigonometry and Triangle Questions

    Gents, Thanks for all the guidance in the past with my work and brothers too. Can anyone help with these , see file attached
  38. D

    Series containing trigonometry

    Homework Statement Determine whether the series [3+cos(n)]/n from n=1 to infinity is convergent or divergent. Explain your reasoning and demonstrate that any conditions required to use a particular test are satisfied. Homework Equations Any series tests: ratio test, alternating sequence...
  39. Saitama

    MHB Can You Crack This Advanced Trigonometry Problem?

    Evaluate: $$\frac{1}{\cos^210^{\circ}}+\frac{1}{\sin^220^{ \circ }}+\frac{1}{\sin^240^{\circ}}-\frac{1}{\cos^245^{\circ}}$$
  40. M

    How to Find the Area of a Triangle Using Basic Trigonometry?

    We got a circle with a radius R. From a distance D from the centerpoint a line is inserted at an offset angle A1 from a line drawn though the centerpoint C of the circle, see the picture below. http://cdn.imghack.se/medium/0861cdab13b8957018f8e167342f2b8e.png I would like the are of...
  41. R

    Trigonometry Limit of sinθ/θ without L'Hopital's Rule

    Homework Statement Find the limit Homework Equations lim θ→ ∏/6 (sinθ - 1/2)/(θ - ∏/6) The Attempt at a Solution well, if you substitute the values, it gives 0/0, but that means that is undefined and that's not the answer. according to my book the answer is √(3)/2 and I am not supposed to...
  42. T

    MHB Trigonometry question: order of operations

    Hello I have -csc^2 x Is this the same as -(cscx)^2 or (-csc x)^2? Thanks, Tim
  43. M

    Can't find any trigonometry textbooks under the math section

    Hi, I've looked under the mathematics textbook section on this site and I can see algebra and geometry but not a single trigonometry book... Is trigonometry normally covered in algebra books something? My trigonometry is really quite terrible and I know the absolute basics so I'm looking for...
  44. MarkFL

    MHB Salim's question at Yahoo Answers regarding trigonometry and circular sectors

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  45. MarkFL

    MHB Rahul's question at Yahoo Answers regarding hyperbolic and circular trigonometry

    Here is the question: I have posted a link there to this thread so the OP can see my work.
  46. B

    Trigonometry - Associated Acute Angles

    Hello, i'm doing some revision and working through the textbook my course follows and have a small problem. The question is an incomplete table of values for sinθ, cosθ, tanθ, \alpha and θ. I have to work out the blanks using what is given. I thought I knew the correct method of doing...
  47. S

    Algebra 2 Trigonometry textbook recommendation

    Are there any well-written algebra 2 trig book that gives understandable contents for beginners?
  48. S

    Find the value of trigonometry

    Homework Statement Find the exact value of cos 247o+sin 293o Homework Equations trigonometry identities The Attempt at a Solution The furthest I can get is: cos 247o+sin 293o = cos 247o - cos 23o = -2 sin 135o sin 112o = -√2 cos 22o Then stuck...
  49. C

    Trigonometry problem involving cylinders.

    Homework Statement Three cylinders are placed in contact with one another with their axes parallel. The radii of the cylinders are 3, 4 and 5 cm. An elastic band is stretched around the three cylinders so that the plane of the band is perpendicular to the axes of the cylinder...
  50. C

    Solve Trigonometry Equation | 2sin3a=sqrt(2) | Geometrical vs Symbolic Methods

    Hi, I have the following equation : 2*sin3a=sqrt(2) I was able to solve it in a geometrical way(giving 6 solutions.) but I have no idea on how to solve it in a symbolic way...(which would take clearly less time to do ) Is there any way ? thank you
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