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. F

    Trigonometry question find range

    guys , following is the problem (sinx)^4 + (cosx)^4 and (sinx)^6 + (cosx)^6 they are asking for the range for each of them i really have know clue how to solve this...any sugeestion please?...thanks for reading this!
  2. R

    Trigonometric Equation Simplification in the Interval [-pi, pi]

    Homework Statement Find the solution of 2(cos x + cos 2x)+sin 2x(1+2cos x)=2 sin x in the interval [-pi, pi] The Attempt at a Solution Simplifying: 2 (cos x- sin x)+ sin 2x +cos 2x +2sin 2x cos x=0 2 (cos x- sin x)+ sin 2x +cos 2x +sin 3x+sin x=0 cos 2x+2cos x+sin 2x-sin x+sin...
  3. R

    Proving y-z=a-c using tan x equation | Trigonometry Homework Help

    Homework Statement If tan x =\frac{2b}{a-c} y=a.cos^{2} x + 2b.sin x.cos x+ c.sin^{2} x z=a.sin^{2} x - 2b.sin x.cos x+ c.cos^{2} xProve y-z=a-c The Attempt at a Solution Assuming that the result to be proved is true; add y and z y+z=a+c and from the result to be proved y-z=a-c From this...
  4. R

    Solve Basic Trigonometry Homework: m^2+n^2=cosec^2θ

    Homework Statement If m^{2}+m' ^{2}+2mm' cos \theta=1 n^{2}+n' ^{2}+2nn' cos \theta=1 mn+m'n'+(mn'+m'n)cos \theta =0, then prove that m^{2}+n^{2}=cosec^{2} \theta The Attempt at a Solution I have tri a lot but its difficult to eliminate m' or n' If I add the first to...
  5. J

    Trigonometry equation, principal value(i dont get this at all)

    1.Solve the following for the principal values of the indicated variable. 2. 3cos x-1=2 3. 3cosx - 1 = 2 3cosx+1=0 im not sure what to do from here, I would ask a teacher or a tutor but it is summer work for a calculus course and i forgot what to do. I have looked in a...
  6. redtree

    Complex Trigonometry Question

    Suppose y = f(x) * sin (kx), where k = wavenumber. If \int y*dy = 3*kx, solve for f(x)
  7. S

    Trigonometry - Hot Air Balloon - Homework Question

    Homework Statement Hello all, I am having trouble with the following homework question using trigonometric formulas and the Sine Law. Here is the problem: Jack spotted a hot air balloon from his house at angle of elevation 57 degrees. Jack's friend who lives 26 km from Jack's house spotted...
  8. T

    Solve Trigonometry Equation: 4cosec(X) - 3sec(X) = 4cos(2X)

    Okay guys, this equation is bothering me and I have no idea how to start: 4cosec(X) - 3sec(X) = 4cos(2X)
  9. L

    Rewriting in terms of another (Trigonometry)

    Yay, finally our Trigonometry final is almost here. I'm taking the test this tuesday, and have been reviewing today. One thing I've had a lot of trouble with is finding the correct sign on problems where I have to rewrite a trigonometric identity in terms of another. For example: Write...
  10. H

    Trigonometry: find minum of y=Tan(x)^p+Cot(x)^q

    Homework Statement suppose p and q are positive rational numbers with the condition : 0<x<Pi/2 find the minimum y=Tan(x)^p+Cot(x)^q Note:with trignonometry Homework Equations The Attempt at a Solution
  11. R

    Need some clarification in regards to trigonometry

    Need some clarification in regards to trigonometry... Homework Statement For some reason, I am not seeing the cause of this. In attached problem 1, the Forces of x are described with a cos while forces of y are described with sin. In the second problem, the forces of X use sin and the...
  12. P

    How to Solve a Trigonometry Exam Problem with tan(5x) = tan(3x)

    I'm preparing for an entrance exam and i have this problem that is puzzling me. tan(5x) = tan(3x) I suppose i should start off by: sin(5x)/cos(5x) = sin(3x)/cos(3x) but i don't know what method to use. Should i break everything down to a single x? Please give me a hint how to start.
  13. R

    Can a Mathematical Formula Predict Missile Collision in Computer Games?

    I've been given a problem by a chap on another forum, to do with making a computer game. The guy wants a missile pre-aim system (a little like clay pigeon shooting), where the target's angle in degrees and speed in pixels-per-frame are used in conjunction with the missile's own speed to...
  14. P

    Trigonometric Inequality Solutions for x

    Homework Statement Find the solutions for x: sinx<\frac{\sqrt{3}}{2} Homework Equations The Attempt at a Solution Will the solution for x be x\in (\frac{-\pi}{2} , \frac{\pi}{3}) ?? or x\in (\frac{5\pi}{6} , \frac{-\pi}{2}) or x\in (\frac{5\pi}{6} , \frac{\pi}{3})
  15. P

    Trigonometry Circular and Inequalities: Homework Statement and Solution Attempt

    Homework Statement I have one trigonometry circular, like on this "[PLAIN 00211.jpg"]picture.[/URL] On the picture there are pi/2 and -pi/2. Also I have another picture with inequality which "[PLAIN 00211.jpg"]I need to solve.[/URL] Homework Equations The Attempt at a Solution...
  16. C

    Solving Trigonometry Equation Algebraically

    [SOLVED] trigonometry math 30pure Homework Statement a student is given the following sinusoidal 2 sin^2 (x)-5sinx=3 Homework Equations 1) Determine the solution to the equation , defined on the domain using a graphical approach over the domain 0 \leq x \leq 2 \pi. Give solutions as...
  17. P

    How Do You Solve Trigonometric Inequalities Involving Sin, Cos, and Tan?

    Homework Statement Find the values for x. 3sin^2x - 3sinxcosx + 2cos^2x > 1 Homework Equations The Attempt at a Solution 3sin^2x - 3sinxcosx + 2cos^2x > 1 3sin^2x - 3sinxcosx + 2cos^2x > sin^2x+cos^2x 2sin^2x - 3sinxcosx + cos^2x > 0 What to do next?
  18. E

    Implicit Derivatives - Trigonometry

    Hello hello everyone... I have a problem that I've been trying to figure out for a couple of days now. Its a question off of an assignment, and I have been busting my balls(excuse my french) with no results. HELP would be GREATLY appreciated...lthis is the question at hand: xsin(y) + x^3...
  19. O

    Trigonometry Problem Solving Book: Strengthen Your Skills

    I am currently trying to strengthen my trigonometry skills and am therefore looking for a trigonometry problem solving book which contains practice problems and goes very in-depth. Does anyone know of any books which could help me with this?
  20. P

    How can logarithms help solve an equation involving trigonometric functions?

    4^{sinx} = \sqrt[cosx]{2} I use logarithmic and i get : sinx * log(4) = (1/cosx) * log(2) sinx*cosx = log(2)/log(4) what should i do next?
  21. B

    Solve Trig Expressions: Inverse Sin and Tan -1/2, Inverse Tan 3/4

    Homework Statement find the exact value of each expression tan[inverse sin(-1/2) - inverse tan 3/4] Homework Equations i know what the answer is because its in the back of the book but i don't know how to solve it and i asked the teacher and he doesn't help anyone. The Attempt at...
  22. D

    Trigonometry - finding the appropriate angle

    Homework Statement "Find the least positive value of the angle A for which: cosA = sinA and both are negative." Im having some trouble on this one as usually i would be given cosA=-0.2 or something but this has no figures... Any help?
  23. G

    (problem) Spherical trigonometry and star declination

    I am looking for a general approach for a type of problems as follows... Certain circumpolar star has a maximum azimuth A given for example as an angle from North to East and from North to West. Whats the declination of that star? The problem looks like this: draw a celestial sphere and...
  24. D

    Explanation:Trigonometry: Simplifying (cos A + 1) / cos A Step by Step

    [SOLVED] Trigonometry cos A + 1 My little sis needs help w/ the following problem for her homework and to tell you the truth, aside from the fact that I'm too busy I have no idea how to explain this to her step by step. I would appreciate an explanation on how to solve it -- a solution would...
  25. G

    Finding the Exact Values of sinx and cosx in Trigonometric Equations

    If tan2x=(-24/7), find the exact value(s) of sinx and cosx Working out the answers by hand, I get sinx = ±3/5, ±4/5 cosx = ±3/5, ±4/5 But by actually calculating x and plugging it into sinx and cosx, I get sinx = 3/5, 4/5 cosx = 3/5, -4/5 I'm pretty sure that the latter...
  26. rocomath

    Finding X: Solving for Points on a Circle with Given A and B Values

    Two points, A and B, are given in the plane. Describe the set of points X such that: AX^2 + BX^2 = AB^2 I'm not really sure how to start this off. I've drawn the circle and a line going from A to B with a midpoint AB at the origin (AB). I also, solved for X which is...
  27. A

    How Do You Determine the Period of a Combined Sinusoid in Trigonometry?

    Hiya, I'm really curious to know the rules of combining trig functions, say if: y = sin(x) + cos(2x) _How would I determine the period of the sinusoid (if it IS one) Is there a mthod of predicting if two sinusoids will compose another sinusoid, if there is I'm missing it. My textbook...
  28. R

    How Do Cosine and Sine Relate to Arctan in Trigonometry?

    Why is cos(arctan x) = 1 / root(1+x^2) and sin(arctan x) = x / root(1+x^2)? I would greatly appreciate help. I'm studying for physics and this came up in one of the solutions. Thank you.
  29. R

    Trigonometry question solving help

    Homework Statement Use the algebraic method to write √2 sin x - √2 cos x in the form kcos(x + ϕ) where k>0, 0≤ ϕ ≤ 2π Homework Equations auxiliary form?? The Attempt at a Solution my working out: 1st: A= √2 B= -√2 K = √a^2 + b^2 = √(√2)^2 + (-√2)^2 = √2+2 = √4 =...
  30. C

    Help with Trigonometry: Solving sinx + sin(x/2) = 0

    Hi. Could someone please help me with the following question? I would really appreciate any help as I am completely stuck at the moment. Solve sinx + sin(x/2) = 0 when x is between (and including) 0 and 360 degrees. Thank you. Cathy
  31. T

    Trigonometry, different products of sine and cosine

    Homework Statement There is a right angled triangle, with the following angles, a, b, and 90deg. If a < b, how many different values are there among the following expressions? sin a sin b, sin a cos b, cos a sin b, cos a cos b Homework Equations The Attempt at a...
  32. S

    Elementary Trigonometry, Help with

    Hello, I have been trying to solve this type of question but the results of my efforts are frequently disappointing. Since this is considered elementary and simple I have no doubt that someone can help me with this: Solve arcsin (3/5) + arctan (1/7). What if it had said 641/19 instead of...
  33. K

    Solving an Angle with Trigonometry

    edit- nevermind i got it okay what i figured so far is that the angle i am looking for is 30 degrees, b/c that bottom angle is 45, so the other angle total should be 45. and then i subtracted 15 and got 30. so i am thinking that the component that is suppose to be tangent would be 2cos30=Ay...
  34. C

    Solving Trigonometry Problem: 2 Variables, 2 Equations

    I've been really stumped by this one from my math class. It's a two variable trig. question with two equations. I believe there simultaneous but I'm not sure 3 = 1.2(cosx) + v(cos30) 0 = 1.2(sinx) - v(sin30) Solve for the values of x & v Please explain how you got your answer or...
  35. A

    Trigonometry sin and cos question

    My teacher told me that C sin(k x) + D cos(k x) = F sin(k x+gamma) if neither C nor D is 0 (gamma is a phase angle). How do you derive the expression on the right of the equal sign from that on the left?
  36. rocomath

    Prove Heron's Formula (Trigonometry)

    Homework Statement If a, b, c are the lengths of the sides of a triangle, then the area K of the triangle is given by K=\sqrt{s(s-a)(s-b)(s-c)}, where s=\frac{1}{2}(a+b+c). The number s is called the semiperimeter. Prove Heron's Formula. Hint: Use the area formula K=\frac{1}{2}bc\sin\phi...
  37. rocomath

    Trigonometry, Prove the Identity and more

    Homework Statement Prove the identity 11. 1 - co5xcos3x - sin5xsin3x = 2sin^2x 50. ln |secx + tanx| = -ln |secx - tanx| 52. The following equation occurs in the study of mechanics: \sin\theta = \frac{I_1\cos\phi}{\sqrt{(I_1\cos\phi)^2 + (I_2\sin\phi)^2}}. It can happen that I_1 = I_2...
  38. B

    Trigonometry Triangle Help: Finding Unknown Angles and Sides

    First off, I was just moved up a grade (about 2 week ago) and the class is studying trigonometry. Homework Statement I have a triangle: Hyp = 10m Opp = 4m Adj= Unknown Feta = Unknown And I need to find feta. Homework Equations ? The Attempt at a Solution Well, I have...
  39. P

    Help with Trigonometry equation

    What is the algebraic method to get from X = (pi)/4 + 2(pi)K into this form => X = (pi)/4 + (pi)/2K ? These are the general equations for all solutions to this original equation: 6 sin^2 X-3=0 , I can understand how to get the general equation graphically can someone show me how to get...
  40. B

    Is it Correct to Divide Both Angles by 2 in Trigonometry?

    cos(2x)=2cos^2(x)-1 what algebrical rule guarantees me thet is right to divide both angles for 2: cos(x)=2cos^2(x/2)-1
  41. J

    What is sin (x + (pi/4)) when sin x = 1/2?

    Simple trigonometry... Just some simple Trigonometry... If sin x = 1/2, then what is sin (x + (pi/4)), if x is greater than or equal to 0 and less or equal to pi over 2? Method?
  42. B

    Trigonometry - Finding degrees of triangle

    I'm having problem with this question: From a point A, three straight lines are drawn to points R, S, T so that TRIANGLE ART is right-angled and points R , S, T are collinear. If AR = 12, AS=13, AT=37, determine the area of TRIANGLE AST. Is it ok to assume RAS and SAT is 45 degrees?
  43. D

    Advanced Trigonometry: Solving for CX in a Triangle with Area 56.4 (3sf)

    I found the area of this triangle to be 56.4 (to 3sf) easily but i can't work out the length of CX. any ideas?
  44. K

    Online texts in algebra 2 and trigonometry?

    do you guys know of any good online textbooks for high school-level algebra 2/trigonometry? the only thing that google gives me is either algebra 1 or college level lecture notes. how effective do you guys think online resources are for studying ahead
  45. H

    Is 180 a Valid Solution for the Trigonometry Equation in Part B) ii?

    in part b) i of a question, i was asked to prove that (1-cos2x)/sin2x is equivilent to tanx and so i did. then in part b) ii i was asked to varify that 180 is a solution of x for: sin2x = 2 - 2cos2x i took the 2 out; sin2x = 2(1 - cos2x) and saw similarities to part i, so i divided by...
  46. A

    Solve Trigonometry Puzzle with P, S and H

    Trigonometry "puzzle" If we know the perimeter P of a triangle, a side S of it, and the height H down on the line going through S, then we have uniquely determined the triangle. It is not wholly trivial to derive the expressions for the other two sides in terms of P,S and H.
  47. I

    Imposibly trigonometry question

    I've been staring at this question for about 4 hours and i am conviced there is some missing data in the question because its just impossible. this is the question "a uniform strip of wood 5.0 cm wide frames a trapezoidal window, as shown in fig 4.84. Find the left dimension "x" of the...
  48. W

    How Does Tan A + Tan C Equal b^2/ac in a Right Triangle?

    ABC is right angled at B. Prove that tanA+tanC=b^2 / ac Ok so far I've got that tan A= a/c and tanC=c/a and then when i try to add those together i get (c^2)(a^2)/ac , but how can (c^2)(a^2) = b^2 all I've thought of is pythagorus's theorem. But for it to equal b^2, a^2 has to be...
  49. J

    How Does Trigonometry Relate Voltage Levels in Transmission Lines?

    The voltage E applied to the sending end of a high-pressure transmitting line is connected to the voltage e at the receiving end by the equation E^2=(e*cos(x) + a)^2 + (e*sin(x) + b)^2, where a and b are constants. Expand the right-hand side of the equation and by expressing a*cos(x) +...
  50. W

    Binomial Theorem and Induction with Trigonometry

    Ok i need help to calculate the co-efficients of certain terms in the binomial expansion for example: (3 + (5/X)^2)^10 what is the coefficient of x^8? I hope that question works sorry if it doesn't i did just make it up then... if you know of any like it please help! also, an...
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