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. H

    Trigonometry Help: Evaluating sin2y & cos2y

    Homework Statement If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and pi/2, evaluate the expression. sin2y cos2y Homework Equations 2siny = 2siny*cosy? cos2y = cos^2 y - sin^2 y? The Attempt at a Solution I think sin2y goes to 2siny*cosy. I know what sin x...
  2. M

    Algebra applied to Trigonometry problem

    Homework Statement tansquaredB=4 solving for B Homework Equations This is algebra applied to Trigonometry, through simplification, to arrive at several different answers involving the degrees of angles. I hope this applies to Physics since physics is "applied Mathematics"...
  3. B

    Trigonometry differentiation problem

    Homework Statement Differentiate the following cos^2 x The Attempt at a Solution \frac{d(cos^2 x)}{dx} = 2 (-sin^{2-1} x).\frac{dx}{dx} = 2 (-sin x).1 = -2 sin x But the answer given is- -2 cos x sin x Can you please tell me what's wrong !
  4. C

    Trigonometry Question: Find the max and min.

    Homework Statement Find the maximum and minimum values of 4cos\theta-3sin\theta. Homework Equations I have no idea. The Attempt at a Solution I have no idea how to do this question Please help me!
  5. Monocerotis

    Trigonometry angle - calculation failed, can't explain.

    Homework Statement I have to find the measures of the angles x & y. Homework Equations Sine Law Cosine Law The Attempt at a Solution First thing I tried to do was find the measure of the angle @ A. a/SinA = c/SinC 66/SinA = 25/Sin10.5 and then I end up with 28...
  6. B

    Wording of a Trigonometry Problem

    Hi, This is a problem that has been very confusing for me and I feel it could be because I am misinterpreting the wording: A tree standing (vertically) on a slope inclined at an angle of 11° to the horizontal casts a shadow of length 15m up the slope. If the angle of elevation of the sun...
  7. R

    Proving sin18 = √5-1/4 without Calculator: Double-Angle Formulae Method

    HELP! trigonometry Homework Statement without using calculator: prove that: sin18 = √5-1/4 Homework Equations Double-angle formulae sin 2a = 2sin a.cos a cos 2a = cos^2a - sin^2a = 1 - 2sin^2a = 2cos^2a - 1 sin^2 a + cos^2 a=1 The Attempt at a Solution let 18=a sin a = sin(90 -...
  8. C

    How Can You Solve csc(6b+π/8) = sec(2b-π/8) in Trigonometry?

    Determine an exact value of b such that csc(6b+π/8)=sec(2b-π/8). Just to clarify, π is pi. This question deals with equivalent trigonometric expressions. I have absolutely no idea how to solve this problem. Please provide me with explanations. Thanks in advance.
  9. H

    Trigonometry Problem: Finding Length of Vector a = (-2sint, 0, -2cost)

    Homework Statement a = 1/sqrt(29) * (-2*sint, 0, -2*cost) length of a is? Homework Equations The Attempt at a Solution ignoring 0, we have sqrt{[(-2*sint)/sqrt(29)]^2 + [(-2*cost)/sqrt(29)]^2}. I get 2/sqrt(29) but answer is [2*sqrt(2)]/sqrt(29). Can anyone do this step by step...
  10. H

    What is the length of (-4pi sin(t), 4pi cos(t), 1) in trigonometry?

    Homework Statement x = (-4\pisin\pit, 4\picos\pit, 1) what is the length of x?Homework Equations The Attempt at a Solution Well, I do realize that length of something is calculated by sqrt(x^2 + y^2) etc. However, when I plug in the numbers above, I get sqrt(16\pi^3 + 1), but the answer is...
  11. C

    Do I integrate it using Trigonometry substitution?

    Dear all, I would like to evaluate \int\frac{1}{1-2sin\left(x\right)}dx Firstly, I make use of the Weierstrass substitution method by letting: u=tan\left(\frac{x}{2}\right) and therefore sin\left(x\right)=\frac{2u}{1+u^{2}} and dx=\frac{2}{1+u^{2}}du Eventually I can...
  12. I

    Need advice on how to study trigonometry

    I'm currently in first year calculus, and I'm having trouble remembering all my trig for use in derivatives. I have some stuff memorized, obviously soh cah toa, and the derivatives of the six trig functions. i.e. derivatives of sinx = cosx cosx = -sinx tan = sec^2(x) etc... but...
  13. H

    Trigonometry Problem: Solving for Unknowns in a Collision Scenario

    Homework Statement In a certain collision problem the kinematics are determined by the following three equations: u=u1cos(@) + SQRT(2) * u2 u1sin(@)=SQRT(2) * u2 0.5mu^2=0.5mu1^2 + 0.5(2m)u2^2 Use the first two equations to express u1 and u2 in terms of u, sin(@) and cos(@). Then substitute...
  14. 1

    Trigonometry Problem: Finding Distances in Sodium Chloride Crystal Structure

    1. Homework Statement A drawing shows sodium and chloride ions positioned at the corners of a cube that is part of the crystal structure of sodium chloride. The edge of the cube is 0.281nm in length. Find the distance between the sodium ion located at one corner of the cube and the chloride...
  15. 1

    Calculating Distance Between Ions in Sodium Chloride Crystal Structure

    Homework Statement A drawing shows sodium and chloride ions positioned at the corners of a cube that is part of the crystal structure of sodium chloride. The edge of the cube is 0.281nm in length. Find the distance between the sodium ion located at one corner of the cube and the chloride ion...
  16. D

    Advanced study of trigonometry

    I was just wondering if anyone could suggest information about the advanced study of trigonometry. I am contemplating getting a degree in mathematics, and I'm currently trying to master the basics of trigonometry in preparation for taking cactus. In looking at all the courses I'll be taking...
  17. D

    Find the Second Solution for sinx = A | Trigonometry Question

    Homework Statement Suppose that x=7pi/23 is a solution of the equation sinx= A where A is some constant. Then A must be equal to [blank], and the other solution of the equation in the interval [0,2pi] must be x = [blank]. The Attempt at a Solution So I've plugged the value into my...
  18. R

    Trigonometry Help: Find Largest Angle for Sine and Tangent Agreement

    Homework Statement For small angles, the numerical value of sin theta is equivalent to tan theta. find the largest angle for which sine and tangent agree. Homework Equations I do not think a equation is need to answer this question. The Attempt at a Solution I honestly couldn't...
  19. X

    Need Book Suggestion for High School Algebra and Trigonometry

    Hi, I need a good book for high school Algebra. If possible, Algebra and Trigonometry both in one book. By High School, I mean for age 15-17years. :P I have chosen Algebra and Trigonometry (3rd Edition) by Beecher/Penna/Bittinger. I think its a good book. Please suggest me more books...
  20. Y

    Trigonometry question, Finding coordinates of 3rd point

    Heres the situation, I have a triangle in which i found all 3 interior angles. I also have the length of all the sides and the coordinates of 2 points. I just need to find the coordinates of the 3rd point I am missing. Is there some formula i need to use for this?
  21. T

    Trigonometry homework: find area of triangle with known lengths

    Homework Statement i need to find angle BDC and side BC when given that AB = 60m BAC = 64 AC = 124 BD = 130 CD = 145 and to find the area of the whole plot Homework Equations The Attempt at a Solution i have worked out side BC = 111.59 by using the Co-sine rule a^2 =...
  22. S

    Trigonometry Help: Understanding 1/2^2 in Terms of Sine, Cosine, and Tangent

    Okay, I must admit, my trigonometry is rather awful... anyway, I would like to write out what 1 / 2^2 is equal to in terms of sine, cosine, tangent, and the like is the following correct, or how do I write it correctly (or what would be the correct figures for 0.5^0.5): 0.5^0.5 = a...
  23. F

    How can trigonometry be used to calculate distance in physics problems?

    Homework Statement Bob heads out into a lake at an angle of 36 degrees, with respect to the shore. If his boat is capable of a speed of 1.7 m/s, how far from land will he be in 7 min and 23 s? Answer in units of m. Homework Equations I have no idea what equation would work for this...
  24. F

    Calculating Coordinates on a Sphere Using Trigonometry

    Can someone just check my maths to see if this is correct. Hopefully, this should give the coordinates for a point on a sphere? x = radius x cos(vert angle) x sin(hoz angle) y = radius x cos(hoz angle) z = radius x sin(vert angle) x sin(hoz angle)
  25. J

    Trigonometry Identity problem I been trying to solve all day

    Homework Statement solve 3cos(x) + 3 = 2 sin^2(x) where 0 <= x < 2piHomework Equations The Attempt at a Solution 3(cos(x) + 1) = 2 sin^2(x) 3(cos(x) + 1) = 2 (1- cos^2(x)) I've tried this variation, and a couple others but it just does not pan out. Please help. Oh yeah we have a real...
  26. C

    Solving Trigonometric Equations: Grade 12 Homework Help | Unit Circle Method

    Homework Statement Solve the following equation: (2sinx-1)(tanx-1) = 0 0<x<2pi The answers are listed as : pi/6, 5pi/6, pi/4, 54/4 Homework Equations I'm told the unit circle is used. The Attempt at a Solution I'm attempting to learn this from dijointed class notes for...
  27. S

    Understanding Spherical Trigonometry: What is it and How is it Used?

    Currently, my knowledge of mathematics includes topics through Calculus, Number Theory, and a bit of Linear Algebra. However, what I'm really interested in learning is spherical trigonometry. I understand that spherical trig has diverse apps in astronomy, but that's about the extent of my...
  28. K

    Failing trigonometry = the death of a amatuer physicist

    I feel so shamed of myself. I don't know who to blame. The teacher gives the exact same lessons on the book, but never follow how you should answer your trig. problems. I studied all through the week and even late at night. I got a C in the class, but I really want to be a physicist because I...
  29. A

    How Do You Simplify Trigonometric Expressions Using Identities?

    Trigonometry Basic (URGENT) please help ! Homework Statement SIMPLIFY: sin(x)/cot^2(x) - sin(x)/cos^2(x) Homework Equations Trigonometric identities I think The Attempt at a Solution I got sin(x)cot^-2(x) - sin(x) sec^2(x) ... but the book says the answer is...
  30. N

    Trigonometric Relations for Line Segments with Fixed and Movable Points

    Homework Statement Straight line segments are drawn from the fixed point P1(0,1) and P2(3,2) to the movable point P, with coordinates (x,0)on the positive x-axis. Assuming that 0 ≤ x ≤ 3, show that the angle θ between the two line segments PP1 and PP2 is given by the relation: θ=...
  31. L

    Prove the SAS Triangle Similarity Theorem from Trigonometry

    Homework Statement As given in the title. The law of cosines, the law of sines, or any other aspect of trigonometry may be used. Ultimately, I need to show that when two triangles have two pairs of proportional sides and the included angles congruent, that they are similar - that is, the...
  32. R

    Solve "cos(15)+sin(15)" Without Calculator

    Homework Statement Find the values of the following, without the use of a calculator, cos(15)+sin(15) Homework Equations sin(A±B)= sinAcosB±cosAsinB cos(A±B)= cosAcosB∓sinAsinB The Attempt at a Solution Without the use of a calculator i had to relate back to the 2 triangles which...
  33. S

    Trigonometry, find solutions between [0/2pi]

    Homework Statement solve, finding all solutions between [0,2pi] tanx=3cotx The Attempt at a Solution It looks like a relatively simple problem if one knew what they were doing unfortunately I do not. I am trying to think of this graphically and I figure that the places were tanx=3cotx...
  34. F

    Finding the Angle Using Arcsec in Trigonometry

    Homework Statement arcsec([2 * sqrt(3)] / 3) Homework Equations N/A The Attempt at a Solution I know that this is equivalent to saying sec (theta) = [2 * sqrt(3)] / 3 I don't know how to solve for theta in terms of PI. I know sec = hyp/adj and the opp side I found was...
  35. W

    How can I use information to draw a graph for trigonometric functions?

    1:... 2:... 3:... 4: Y = A cos(Bx+C)+K Y = A sin(Bx+C)+K I know what A,B,C, and K mean.. and I Also understand that I can get the Period from B.. but, how can I use the information to draw the graph? I think I should use critical points, right? If so, what should I typically use...
  36. V

    Finding Coefficients for Vector Equivalence: A Trigonometric Approach

    Homework Statement A screenshot of the problem: http://img246.imageshack.us/img246/9194/homeworkkd6.jpg Homework Equations Not sure... possibly the dot product of two vectors? v*w = a(1)a(2) + b(1)b(2) The Attempt at a Solution Part of the problem is that I'm not entirely sure...
  37. F

    Good book on trigonometry proofs?

    Hey all, I'm looking for a decent, (and preferably cheap) book, or books, on trigonometry. Something that proves some or all the trig equations we're expected to remember in high school stuff (most of which I've forgotten), but it should also leave room for my curiosity so I can prepare for...
  38. X

    What is the value of secx when sinx = -0.40 and tanx > 0?

    If sinx = -0.40 and tanx > 0, then secx, to the nearest hundreth, is A) 0.92 B) -0.92 C) -1.09 D) 1.09 So I figured that sin^-1 = -23.57817848, but I don't know how to get sec, can someone help!
  39. M

    Trigonometry related to Archery

    Intro: Hello, I have spent the last four or so days searching google and this forum and as rich as both are in information and helping. I have found it very hard to get anywhere. Basically I haven't done any Maths/Physics related courses and as a result I am totally stumpped on my Games...
  40. I

    Are complete cycles in trigonometry always 360 degrees?

    Homework Statement When dealing with periods and amplitudes in trigonometry, are all complete cycles (for cosine, sine, and tan functions) considered to be 360(degrees)? I'm just wondering, because I want to make sure now so that I can apply it to the appropriate questions when the time...
  41. M

    Proving the Trigonometric Equation 1-sin2θ/cos2θ = 1-tanθ/1+tanθ

    Sorry but i don't know how to use latex yet or to add mathematical symbols somehow. Homework Statement Prove that 1-sin2θ/cos2θ = 1-tanθ/1+tanθ Homework Equations sin2θ = 2tanθ/1+tan2θ and cos2θ =1-tan2θ/1+tan2θ I have allready proved from a previous exercise those two above so...
  42. T

    Are Secant and Trigonometric Identities Confusing in Calculus?

    Homework Statement I'm currently in cal 1 and we are doing trigonometry identities for review. I can't recall ever seeing a sum/difference formula for secant in precal (1) Prove secant² (4θ) / 2 - secant² (4θ) = secant (8θ) (2) Prove tan(x)/(1-cot(x)) + cot(x)/(1-tan(x)) = sec(x)csc(x) + 1...
  43. L

    Is the Trigonometry Book Wrong? Conflicting Answers for x in secx^2-4=0

    b]1. Homework Statement [/b] Hey, I have a problem that I worked out in a trigonometry book. I got different answers from what the book gave, but I think that I am right and the book is wrong. Could someone please tell me who is right? Homework Equations Okay, they gave me the following...
  44. C

    Limits, L'Hospital's Rule & Trigonometry

    SOLVED, thanks to Dick and viciousp! Homework Statement The question asks: Find the limit. Use L'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If L'Hospital's Rule doesn't apply, explain why. Limit as x approaches pi/2 from the right (+) of...
  45. C

    Trigonometry Review: Conflict Answer, Probably Me

    SOLVED! Thank-you jhicks and Tedjn! I am taking a basic calculus course and have some weaknesses when it comes to trigonometry. In this case, it's pure trig. Homework Statement The question states: "Find all values of x in the interval [0,2pi] that satisfy the equation sin x = tan x"...
  46. J

    Calculating Trigonometric Functions in the Cylinder System

    i got to find the sin and cos of cylinder. in the cylinder system please help me
  47. S

    Trigonometry or components to find the displacement

    1. Homework Statement : Bob walks 360 m south, then jogs 490 m southwest, then walks 360 m in a direction 35 degrees east of north. Use either trigonometry or components to find the displacement that will return Bob to his starting point by the most direct route. Give your answer as a...
  48. A

    Use either trigonometry or components to find displacement

    Homework Statement Bob walks 160 m south, then jogs 630 m southwest, then walks 160 m in a direction 32degrees east of north. a) Use either trigonometry or components to find the displacement that will return Bob to his starting point by the most direct route. Give your answer as a...
  49. S

    Finding the Height of a Gondola Ski Lift Using Trigonometry

    Homework Statement the gondola ski lift at kystone, Corolrado is 2830m long. On avg, the ski lift rises 14.6 degree above the horizontal. How high is the top of the ski lift relative to the base. Homework Equations tan * = ha/h The Attempt at a Solution i just...
  50. D

    Trigonometry Help: Qs 1, 4, 5 - Get Answers Now!

    hey guy I am new to the forum im having a hard time understand number 1, 4, 5. i post all the question for anyone to double check my answers. thanks for the help guys http://img176.imageshack.us/my.php?image=clipimage002ak9.jpg http://img176.imageshack.us/my.php?image=clipimage002ak9.jpg
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