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. N

    What is the angle needed to solve this right triangle?

    The Figure My Attempt at Solution ##\tan{ACB} = \frac{AB}{BC}, \ \tan41.45^\circ = \frac{AB}{10} \Rightarrow AB = 10\tan45.41^\circ \approx 8.83##cm Similarly ##\tan{CBD} = \frac{CD}{BC}, \ \tan32.73^\circ = \frac{CD}{10} \Rightarrow CD = 10\tan32.73^\circ \approx 6.43##cm After this I...
  2. N

    How to Solve a Trigonometry Word Problem Involving Distances

    The sketch: First of all find the length of PQ on i.e $$4 \ inches - 1 \ mile$$ $$1.2 \ inches - x \ mile$$ $$x = \frac{1.2}{4} = 0.3 \ mile = 1584 \ ft$$ Now, I do not understand where shall I draw the horizontal, and the connection between the lengths of the contours, so I'll be grateful if...
  3. N

    Trigonometry - Cricket related word problem

    Hello, I don't know anything about cricket, so I'll be grateful if you help me with constructing a diagram for this problem. Here's my attempt. I looked up on the internet and I pretty much get the idea of pitches and wickets, but still cannot connect everything together. Thank you.
  4. Monoxdifly

    MHB [ASK] Trigonometry Question

    Suppose the angles in triangle ABC is A, B, and C. If sin A + sin B = 2 sin C, the value of 2tan\frac12Atan\frac12B is ... A. \frac83 B. \sqrt6 C. \frac73 D. \frac23 E. \frac13\sqrt3 Since A, B, and C are the angles of triangle ABC, then C = 180° – (A + B) sin A + sin B = 2 sin C sin A + sin B...
  5. J

    Trigonometry Help: Calculating the Angle of Light Entry & Exit

    So what I did first was made the face of the triangle flat and calculated the angle the light entered it. This means the light enters the triangle from the base corner angle (so (180-38.8)/2) of 70.6 degrees. 1sin(70.6)=1.47sin(angle) angle=39.915 Now I need to find the angle it exits. But...
  6. S

    Integration of this trigonometry function

    Is it possible to do the integration? That is the full question I don't know where to start, try to use ##u=\cos x## and also ##\cos^2 (x) = \frac{1}{2} + \frac{1}{2} \cos (2x)## but failed. Thanks
  7. N

    Trigonometry - Horizon Related Word Problem

    Hello! I'm trying to solve this problem. Here's the diagram I tried to make. I have difficulty understanding this math problem.. I've tried to solve the problem using the symmetry of the triangles but I didn't get the right answer, and I can't seem to understand the "concept" of the horizon...
  8. A

    MHB Trig Angles: Equations & Solutions

    I need only equations on this one
  9. Thendi79

    Other Can someone suggest a good trigonometry book to learn trigonometry ?

    I tried the openstax book Algebra And Trigonometry but i wish there was some better books that teaches trigonometry , anything else i should tried to read ?
  10. brotherbobby

    To prove a trigonometric identity with tan() and cot()

    Attempt : I could not progress far, but the following is what I could do. $$\begin{align*} \mathbf{\text{LHS}} & = (\tan A+\tan B+\tan C)(\cot A+\cot B+\cot C) \\ & = 3+\tan A \cot B+\tan B \cot A+\tan A \cot C+\tan C \cot A+\tan B \cot C+\tan C \cot B\\ & = 3+\frac{\tan^2A+\tan^2B}{\tan A \tan...
  11. John Greger

    I Units of trigonometric functions?

    What are the units of the trigonometric functions sinus, cosinus etc? If I take say Sin(0.5), what would the units of the output be?
  12. sahilmm15

    Other High School Trigonometry course

    Can you review this high school trigonometry course. I am having a hard time finding a course about trigonometry for intermediates. I am clear with my basics and want to dive in deep now.Thanks for any suggestions!http://www.mecmath.net/trig/trigbook.pdf
  13. L

    Vectors and Trigonometry Homework Help

    Hey, I am new to this community and I am in need of help with this physics problem. I have used the formula above and the answer I get is 1.43s. The correct two answers are 0.68s and 2.4s. For the Vf the answer is 8.3 m/s.
  14. Monoxdifly

    MHB [ASK] Limit of Trigonometry Function

    \lim_{x\to0}\frac{sin2x+sin6x+sin10x-sin18x}{3sinx-sin3x=} A. 0 B. 45 C. 54 D. 192 E. 212 Either substituting or using L'Hopital gives \frac00. Is there any way to simplify it and make the result a real number?
  15. AN630078

    Trigonometry: finding an angle, area and length of sector of a circle

    1. Using the formula for the arc length; s= θr I have endeavoured to find the angle AOB sine both the arc length and radius are known; 11= θ*8 θ=11/8=1.375 rad I actually do not think that this can be correct as it seem to simplistic a response. Have I misinterpreted the question or used the...
  16. Monoxdifly

    MHB [ASK]Solution Set of a Trigonometry Inequation

    The set of real numbers x at the interval [0, 2π ] which satisfy 2sin^2x\geq3cos2x+3 takes the form [a, b] ∪ [c, d]. The result of a + b + c + d is ... a. 4π b. 5π c. 6π d. 7π e. 8π What I've done thus far: 2sin^2x\geq3cos2x+3 2sin^2x\geq3(cos2x+1) 2sin^2x\geq3(cos^2x-sin^2x+sin^2x+cos^2x)...
  17. S

    B What is the connection between the Law of Cosines and Euclid's teachings?

    I
  18. chwala

    Transformation of trigonometry functions

    kindly note that this solution is NOT my original working. The problem was solved by my colleague. I have doubts with the ##k## value found. Is it not supposed to be ##k=0.5?## as opposed to ##k=2?##. From my reading on scaling, the graph shrinks when ##k## is greater than ##1## and conversely.
  19. mcastillo356

    B Electromotive force and trigonometry

    Faraday's law: \epsilon=-N\dfrac{\Delta{\phi}}{\Delta{t}}=-N\dfrac{\Delta{(BA\cos{\theta})}}{\Delta{t}}=-N\dfrac{\Delta{(BA\cos{(\omega t)})}}{\Delta{t}} Applying calculus \epsilon=NBA\omega\cos{(\omega t)} Shouldn't it be \epsilon=NBA\omega\sin{(\omega t)}, just if I apply limits? Thanks
  20. chwala

    Proof of Trigonometry Identity: a^2b^2=sin^2θcos^2θ

    ##a^2= \frac {sin^4θ} {cos^2θ}## ##b^2=\frac {cos^4θ} {sin^2θ}## therefore ##a^2b^2= sin^2θ. cos^2θ##...1 and ##a^2+b^2+3= \frac {sin^6θ + cos^6θ + 3 sin^2θ cos^2θ} {sin^2θ cos^θ}##...2 multiplying 1 and 2, we get, ##sin^6θ + cos^6θ + 3 sin^2θ cos^2θ## how do i proceed from...
  21. Marso

    How Do You Prove Two Triangles Are Similar?

    I have tried multiple methods to solve this but have been unsuccessful at every attempt. The apparent correct answer is:
  22. S

    Finding the sum of this trigonometry series

    I got answer to (a), which is 3/4 sin thteta - sin ((3^(n+1)) theta) / (4 . 3^n) but I do not know how to use this result to prove next question. I tried to change theta into pi/2 - theta so that sin change to cos or vice versa but not working. Thanks
  23. Monoxdifly

    MHB [ASK] Proving Trigonometry 2sinα+2sinβ+2sinγ=4sinαsinβsinγ

    If \alpha+\beta+\gamma=180°, prove that 2sin\alpha+2sin\beta+2sin\gamma=4sin\alpha sin\beta sin\gamma! All I knew is that sin(\beta+\gamma)=sin(180°-\alpha)=sin\alpha, but I think it doesn't help in this case.
  24. RichardWattUK

    I Translating points on the axes

    Summary: I need to translate points on coordinate axes as part of a calculation process Hello everyone, I've created the diagram below to try and explain what I am trying to do as part of an existing software app that's used to generate profiles and programs to drive a CNC machine to grind...
  25. X

    B Calculating trigonometry without calculator?

    Speaking of trigonometry without a calculator, I usually only memorizes the trig values of 30°, 45° and 60°. then by I can apply basic equations and applying to polygons or other geometry shapes I can get trig values for angles like 15° Or 75°. When people have enough time, people on Wikipedia...
  26. C

    Trigonometry (re-moved to Precalc Math Homework)

    Homework Statement: (cos2A -1)/sinA +sin2A/(cos2A+1)*cosA=__________________ Homework Equations: sin2A=2sinAcosA cos2A+1=cos^2A cos2A-1=sin^2A (cos2A -1)/sinA +sin2A/(cos2A+1)*cosA [cos^2(2A)-1 +2sin^2(A)cos^2(A)]/sinA(cos2A+1) [-sin^2(2A) + 2sin^2(A)cos^2(A)]/sinA(cos2A+1) I can't proceed...
  27. PhamCy

    Trigonometry solutions Question

    Summary: https://www.physicsforums.com/threads/trigonometry-question.977263/ Here's the question. Find the solutions of the equation tan(x)=2cos(x)+1 if 0 ≤ x ≤ 2π. I know this question can be solved by observing the graph but is there any other ways (like algorithms OR some Trigonometry...
  28. C

    Trigonometry: if a = sinx+cosx and b=tanx+cotx, then a(b^2-1)-2 = ?

    b^2-1= tan^2(x) + cot^2(x) + 2 -1 b^2-1= sin^2(x)/cos^2(x) +cos^2(x)/sin^2(x) -1 b^2-1=[sin^4(x) +cos^4(x)]/sin^2(x)cos^2(x) -1 b^2-1=[1-sin^2(x)cos^2(x)]/sin^2(x)cos^2(x) -1 a(b^2-1)=sinx+cosx {[1-sin^2(x)cos^2(x)]/sin^2(x)cos^2(x) -1 } I am not able to go any further than this step to reach...
  29. B

    MHB Trigonometry: Right-angled triangle

    Hi Guys I need help with this question so if you can help me with the answer please please.
  30. S

    MHB Real world trigonometry problem making furniture

    I'm building a bed bench and I have an interesting trig problem that I can't figure out. I have a rectangle with known values and a parallelogram that bisects it with a known width. Like a board. I want to be able to figure out the angles so I can cut it. I want the board to intersect the...
  31. S

    What is the rotational acceleration of a falling chimney?

    Hi all, I found this problem in a new textbook I'm working through. And my energy conservation equation was ## mg\frac {h}{2} = \frac {1}{2} I ω^2 + mg \frac {h}{2}*sin(55) ## My solution was wrong and after checking why I found that they used cos(35) as the angle. The rest was the same. I'm a...
  32. archaic

    Perfect material for trigonometry

    The illustrations on this website are perfect. http://trigonography.com/toc/ I hope it'll help!
  33. Charles Link

    B A simple trigonometry problem: Put eight coins around a central coin

    I have a simple trigonometry problem. I thought of making this as one of the math challenge problems, but it is almost too easy for that. ## \\ ## It is well known that 6 coins (circles) of equal size can be put around a center coin of the same radius, with the outer coins each touching two...
  34. M

    How to Solve a Derivative Presented in a Non-Standard Format?

    I have attached a word document demonstrating the working out cos i was too lazy to learn how Latex primer works and writing it like I did above would've been too hard too read. I tried to make it as understandable as possible, presenting fractions as ' a ' instead of ' a / b ' . ------ b
  35. QuarkDecay

    Solving a trigonometric equation for the angle

    Homework Statement The equation; 0.966= -0.354sin(φ+60) + 0.935cos(φ+60) and we're trying to find φ. Homework Equations 3. The Attempt at a Solution [/B] (edited) I tried doing ^2; 0.933= 0.125sin2(φ+60) -2*0.331sin(φ+60)cos(φ+60) + 0.874cos2(φ+60) x=φ+60 0.933= 0.125sin2x - 0.331sin(2x) +...
  36. L

    I Finding the coordinates of a point on a sphere

    I have three points: A, B and C, which are all on the surface of the same sphere. I need to find the xyz coordinates of C. What I know: - the radius of the sphere - the origin of the sphere - the xyz coordinates of A and B - the arc distance from A to C and from B to C - the angle between AB and...
  37. W

    MHB Kinematics + Trigonometry Application (Physics 12u)

    Show that the maximum range of a projectile launched with Vi from Yi=0 is 45 degrees. (HINT: sin20 = 2sinθcosθ)
  38. M

    Struggling with Biomechanics? Get Expert Help Here!

    Hello! I am a third year kinesiology student who is struggling with her biomechanics assignment. Mind you, I haven’t studied physics or trigonometry in four years since i left high school so I really need some help.
  39. G

    MHB Need help with Physics with trigonometry problems ?

    3) Hurricane Michael had horizontal winds of Vout = 69 m/s (155 mph). Pair = 1.29 kg/m3. A building with a flat, horizontal roof, Aroof = 200 m2, and Vin = 0 m/s. a) What is the pressure difference, Pin - Pout on the roof. Assume Yin = Yout. b) What is the force acting on the roof, and what...
  40. M

    Solving a Trigonometry Problem: Find u(x,t) Polynomial

    <Moderator's note: Moved from a technical forum and thus no template.> Task: http://snk066.tk/math/Task.png My solution: http://snk066.tk/math/my_solution.jpg What you need to? I need an answer in the form: u (x,t) = (some polynomial) The solution is not really necessary, if someone will...
  41. Nate1

    MHB Trigonometry lighthouse boat problem

    A boat is some distance away from a small lighthouse. The angle of elevation from the boat is 9 degrees. If the boat moves forward 20m, the angle is now 12. Assume the lighthouse is at a rightangle to the boat. Calculate the distance from the boat to the top of the lighthouse before and after...
  42. N

    Trigonometry - Double Angle Identities

    Homework Statement If I have the following relation: tan(2x) = (B/2) / (A - C) but tan(2x) = sin(2x) / cos(2x) How do I obtain an expression for sin(x) and cos(x) in terms of the constants, B,A,C only? Homework Equations cos(2x) = 1- 2 sin^2(x) The Attempt at a Solution [/B] I can't...
  43. Physicsterian

    B Why does the force increase when holding a bag at an angle of 45 degrees?

    Hi, If 2 people are holding a bag at an angle of 45 degrees each, and then only person is going to hold it, it is being said that the force that will have to be applied by that one person will be 1.5 times greater than when he was applying it together with the other. Can anyone explain this or...
  44. P

    Solving absolute values of trigonometry

    Homework Statement Homework EquationsThe Attempt at a Solution 2sin3x=1 OR 2sin3x= -1 sin3x=1/2 sin3x= -1/2 From the unit circle and in accordance with the domain there are 3 solutions (B) But the answer is (C) HOW?
  45. ISamson

    Finding height and area of trapezoid from its legs and bases

    Hello. I am wondering how I can find the area of a trapezoid from its two legs and bases. My problem: ABCD is a trapezium with AB parallel to CD such that AB = 5, BC = 3, CD = 10 and AD = 4. What is the area of ABCD? If we trace a straight line from A down parallel to the height of the...
  46. Jan Berkhout

    How do I do this trigonometry vector calculation?

    Homework Statement A pilot wishes to fly at maximum speed due north. The plane can fly at 100km/h in still air. A 30km/h wind blows from the south-east. Calculate: a) The direction the plane must head to fly north. b) Its speed relative to the ground. Homework Equations Sine Rule...
  47. T

    B How Tall is the Tower in This Classic 1957 Math Problem?

    Here is a problem I found which is from a math class in 1957: A man is standing due East of a tower and notes it subtends an angles of 45 degrees with the tower. He walks South 42.4 feet and the subtended angle is 30 degrees. How tall is the tower? (You are only allowed to use only...
  48. F

    Trouble developing trig expression

    Homework Statement It's not a problem per se, I'm just trying something, so there's no statement. What I'm trying to do it's to prove the forllowing equation but without using the member of the right. (cos(36º) + 1)²/(cos(36º)) = 5cos(36º) There's the trivial answer, using both members, that...
  49. Bobs

    Today, in our class, we received a trigonometric equation

    Today,in our class, we received a trigonometric equation ##\sin^{10}{x}+\cos^{10}{x}=\frac{29}{16}\cos^4{2x}## Here is my attempt:
  50. chwala

    Proving Trigonometric Identities: (sin φ+1-cos φ)/(sin φ+cos φ-1)

    Homework Statement Show that ## {(tan φ+sec φ-1)/(tan φ-sec φ+1)}≡ {(1+sin φ)/cos φ}##[/B]Homework EquationsThe Attempt at a Solution ## (sin φ+1-cos φ)/(sin φ+cos φ-1)##[/B]
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