What is Trig: Definition and 1000 Discussions

The Renewables Infrastructure Group (LSE: TRIG) is a large British investment trust dedicated to investments in assets generating electricity from renewable sources. Established in 2013, the company is a constituent of the FTSE 250 Index. The chairman is Helen Mahy.

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  1. A

    How to Determine Correct Inverse Trig Angle?

    I understand why certain inverse trig functions have two answers. Like for arcsin(0.5), it could be pi/6 or 5pi/6. I know both angles have the same sin value, that they're both on the same horizontal line on a graph of sin, I get all of that, but two questions about it: 1) In cases where...
  2. A

    I Practice With Proofs? (Algebra, Trig, and Calc)

    I'm trying to brush up on my algebra, trig, and calculus, and one thing I know I was always weak on before was proofs. I was never sure what equations would suffice as "proof," and which equations did not. Maybe this is an inane question, and maybe there is a really simple answer to this. I...
  3. T

    A Trig functions and the gyroscope

    Good Morning As I continue to study the gyroscope with Tait-Bryan angles or Euler angles, and work out relationships to develop steady precession, I notice that the trig functions cancel. I stumble on terms like: 1. sin(theta)cos(theta) - cos(theta)sin(theta) 2. Cos_squared +...
  4. C

    Another way to find trig identities

    Using the identity's (1) (2) Gives, Why dose this elegant method work? Many thanks!
  5. C

    Proving trig identities -- Is the method related to the unit circle?

    Why when proving trig identities, Do we assume that r = 1 from ## rcis\theta = r[\cos\theta + i\sin\theta]##? This makes me think that this is somehow it is related the unit circle. Note: I am trying to prove the ##cos3\theta## identity and am curious why we assume that the modulus is 1...
  6. N

    Find an equivalent equation involving trig functions

    Rewrite the given equation, attempt 1: ##2\sin(x)\cos(x) + 2\sin(x) + 2\cos(x) = 0## ##\sin(x)\cos(x) + \sin(x) + \cos(x) = 0## ##\sin(x)(\cos(x) + 1) + \cos(x) = 0##, naaah, can't get any relevant out from here. Attempt 2: ##2\sin(x)\cos(x) + 2\sqrt{2}*\sin(x + \pi/4) = 0## ##\sin(x)\cos(x) +...
  7. chwala

    Comparing Hyperbolic and Cartesian Trig Properties

    I came across this question; i noted that the hyperbolic trigonometry properties are somewhat similar to what i may call cartesian trigonometry properties... My approach on this; ##\tanh x = \sinh y## ...just follows from ##y=\sin^{-1}(\tan x)## ##\tan x = \sin y## Therefore...
  8. Mayhem

    I Adding trig functions with different amplitudes

    The trig identities for adding trig functions can be seen: But here the amplitudes are identical (i.e. A = 1). However, what do I do if I have two arbitrary, real amplitudes for each term? How would the identity change? Analysis: If the amplitudes do show up on the RHS, we would expect them...
  9. karush

    Differentiate ##f(x)=x\cos{x}+2\tan{x}: D/dx ##\tiny{2.4.2}##

    ##\tiny{2.4.2}## Differentiate ##f(x)=x\cos{x}+2\tan{x}## Product Rule ##[-x\sin{x}+\cos{x}]+[2\sec^2]\implies \cos{x}-x\sin{x}+2\sec^2x## mostly just seeing how posting here works typos maybe suggestions what forum do I go to for tikz stuff
  10. chwala

    Proof of the trig identities for half-angles

    I was just checking this out the sin##\frac {A}{2}## property, in doing so i picked a Right-Angled triangle, say ##ABC##, with ##AB=5cm##, ##BC=4cm## and ##CA= 3cm##. From this i have, ##s=6cm## now substituting this into the formula, ##sin\frac {A}{2}##= ##\frac {1×3}{5×3}##=##\frac...
  11. V

    Solving for z in the Equation tan z = 1 + 2i

    Find the values of tan-1(1+2i). We can use the fact: tan-1z = (i/2)log((i+z)/(i-z)). Then with substitutions we have (i/2)log((1+3i)/(-i-1)). Then I think the next step would be (i/2)(log(1+3i)-log(-1-i)). Do we then just proceed to solve log(1+3i) and log(-1-i)? I'm just a little confused...
  12. A

    U-Substitution in trig integral

    ##\int \frac{\csc{x}\cot{x}}{1+\csc^2{x}}dx## Let ##u = \csc{x}## then ##-du = \csc{x}\cot{x}dx## So, ##\int \frac{\csc{x}\cot{x}}{1+\csc^2{x}}dx## ##-\int \frac{1}{1+u^2}du = -\arctan{u} + C## ##-\arctan{\csc{x}} + C## This answer was wrong. The actual answer involved fully simplifying...
  13. BWV

    Worth learning complex exponential trig derivations in precalc?

    This is a pedagogical /time management / bandwidth / tradeoff question, no argument that learning the complex exponential derivation is valuable, but is it a good strategy for preparing for first year Calculus? my 16YO son is taking AP precalc and AP calc next year and doing well, but struggled...
  14. karush

    MHB 7.2.15 Int of trig in a radical

    Evaluate the integral $I_4=\displaystyle\int_{-\pi}^{\pi}\sqrt{\frac{1+\cos{x}}{2}} \, dx $ ok offhand i think what is in the radical is trig identity but might be better way...
  15. benorin

    A Trick to Memorizing Trig Special Angle Values Table

    Continue reading...
  16. srfriggen

    I think the book is wrong about this trig equation

    When solving for x I get the angles 0, pi, pi/2 and 3pi/2. However, I thought I should reject the pi/2 and 3pi/2 values since they are not in the domain of sec^2(x). I am using the opens tax precalc book and their answer does not reject those two angles.
  17. karush

    MHB -7.3.89 Integral with trig subst

    $\begin{array}{lll} I&=\displaystyle\int{\frac{dx}{x^2\sqrt{x^2-16}}} \quad x=4\sec\theta \quad dx=4\tan \theta\sec \theta \end{array}$ just seeing if I started with the right x and dx or is there better Mahalo
  18. kshitij

    Limit calculation involving log and trig functions

    This was the question, The above solution is the one that I got originally by the question setters, Below are my attempts (I don't know why is the size of image automatically reduced but hope that its clear enough to understand), As you can see that both these methods give different answers...
  19. B

    What is the proof for the rare trig identity with tan/tan = other/other?

    Came across this trig identity working another problem and I've never seen it before in my life. I don't need to prove it myself, necessarily, but I would really like to see a proof of it (my scouring of the internet has yielded no results). If someone more trigonometrically talented than myself...
  20. karush

    MHB 8.aux.27 Simplify the trig expression

    $\tiny{8.aux.27}$ Simplify the expression $\dfrac{{\cos 2x\ }}{{\cos x-{\sin x\ }\ }} =\dfrac{{{\cos}^2 x-{{\sin}^2 x\ }\ }}{{\cos x\ }-{\sin x\ }} =\dfrac{({\cos x}-{\sin x})({\cos x}+{\sin x\ })}{{\cos x}-{\sin x}} =\cos x +\sin x$ ok spent an hour just to get this and still not sure suggestions?
  21. karush

    MHB B.2.1.4 trig w/ integrating factor

    $\begin{array}{rl} \textit{Find } \mu(x): &\mu(x) =\exp\left(\int \dfrac{1}{x}\,dx\right)=e^{\ln{x}}=x\\ \textit{multiply thru by x} &xy^\prime+y=3x\cos 2x\\ \textit{rewrite as } &(xy)'=3x\cos 2x \\ \textit{}integrate &xy=\int 3x\cos 2x \...
  22. karush

    MHB -apc.2.2.03 trig product rule

    v=197 If $y=x \sin x,$ then $\dfrac{dy}{dx}=$ $a.\quad\sin{x}+\cos{x}$ $b.\quad\sin{x}+x\cos{x}$ $c.\quad\sin{x}+\cos{x}$ $d.\quad x(\sin{x}+\cos{x})$ $e.\quad x(\sin{x}-\cos{x})$ well just by looking at it because $dx(x) = 1$ elimanates all the options besides b $1\cdot \sin (x)+\cos (x)x$...
  23. F

    I Why is it important to convert angle units when using trigonometric functions?

    Hello, Periodic trigonometric functions, like sine and cosine, generally take an angle as input to produce an output. Functions do that: given an input they produce an output. Angles are numerically given by real numbers and can be expressed either in radians or degrees (just two different...
  24. J

    Can the limit of a quotient of trig functions approach a specific value?

    Hello. Sin and cos separately oscillates between [-1,1] so the limit of each as x approach infinity does not exist. But can a quotient of the two acutally approach a certain value? lim x→∞ sin(ln(x))/cos(√x) has to be rewritten if L'hôp. is to be applied but i can't seem to find a way to...
  25. L

    MHB Solve Trig Identity: Tips & Explanation

    How do I work this out? Can’t seem to get my head around it! Thanks
  26. S

    What is the domain of a trig function with y = 2sin(x)?

    y = 2sin(x) -1≤ sin(x) ≤ 1 -2 ≤ 2sin(x) ≤ 2 so -2 and 2 are the max/min limits but the domain is -π < x ≤ π Do I find the values of x that outputs -2 and 2 and show that they are within the domain ?
  27. chwala

    Integration of a trig function

    This is my first attempt ...
  28. srfriggen

    B Verifying trig identities.... what about when tan is undefined?

    Hello, If I wanted to verify tan(x)cos(x) = sin(x), what about when x is pi/2? LHS has a restricted domain so it can't equal sin(x). Does this equation only work with a restricted domain? Nothing in my textbook discusses that. Thank you
  29. madafo3435

    Help please with this integral involving an inverse trig function

    ## \int_0 ^ {2 \pi} \frac {dx} {3 + cos (x)} ## las únicas formas que probé fueron, multiplicar por ## \frac{3-cos (x)}{3-cos (x)} ## pero no me gusta esto porque obtengo una expresión muy complicada. También recurrí a la sustitución ## t = tan (\frac {x} {2}) ## que me gusta bastante, pero...
  30. C

    MHB Need help understanding phase shift in trigonometric curves

    At what value of α is the curve y=asin2π/λ (x+α) in phase with z=asin2π/λ(x)? My answer booklet says α=1−λx+nλ, but I keep getting α=nλ, where n=0,1,2... I have no clue how to get to the answer shown in the mark scheme. Any insight would be much appreciated!
  31. xyz_1965

    MHB How do trigonometric functions and their inverses relate to each other?

    Take any trig function, say, arcsin (x). Why is the answer x when taking the inverse of sin (x)? Why does arcsin (sin x) = x? Can it be that trig functions and their inverse undo each other?
  32. rxh140630

    Checking this answer regarding a trig problem

    Author gave solution C = \sqrt{2}, ∝ = -pi/4 but plugging C = - \sqrt{2}, ∝ = -3pi/4 into cos(x+y) and leaving the x I get \sqrt{2}Cos(x+3pi/4) = sinx+cosx Is my answer valid as well?
  33. rxh140630

    Question regarding a trig equation

    See the attached image. Apostol gives cos(nθ) = cos((n-1)θ)cos(θ) - sin((n-1)θ)sin(θ), in the middle of the picture, but previous info given does not state how he got this equation. To me it looks like he used the equation cos(x+y) = cosxcosy-sinxsiny
  34. leticia beira

    Finding the derivative of this trig function

    Para f (θ) = √3.cos² (θ) + sen (2θ), uma inclinação da reta tangente, uma função em θ = π / 6, é?
  35. S

    MHB Couple of hard trig questions....

    Hi, I was hoping to get some help on these five questions, I've been stuck on these and any help would be greatly appreciated! 1. Inflation rises and falls in a cyclical manner. If inflation is highest at 4.8% and lowest at 1.3%, what c for the equation y = a sin(k(x + d)) + c? 2. If the...
  36. B

    Cars Collide on a Hill, Conservation of Momentum

    QUESTION: ----------- For the purposes of this problem, we will define the direction of Vehicle A's initial velocity as the positive direction: While driving on a road that is inclined at an angle of 10 degrees above the horizontal, Vehicle A and Vehicle B are in a head-on collision lasting...
  37. L

    MHB Solve trig equation cos(2x+20)=-cos(x-11)

    Kindly assist with this question: Determine the general solutions cos(2x+20)=-cos(x-11)
  38. AzureSekki

    Need help on how they got these numbers -- solution to a trig equation

    Summary:: This is not a homework i just need clarification on how they got those number Any solution involving sine and cosine is my weakness when its advance or intermediate
  39. L

    Where can I find a long list of clearly solved trig integral problems?

    Homework Statement:: I need to develop my instincts on when to use u-sub, integration-by-parts, trig substitution, etc. But, I need to read/see tons of problems actually being solved with these techniques to know which technique to apply quickly. Relevant Equations:: Sorry for the vague...
  40. MichaelRocke

    Trig Identities - Pre-calculus in a Nutshell - Section 4 Question 1

    My latest attempt \begin{align*} \frac{\sin \theta + \tan \theta}{\csc \theta + \cot \theta} = \\ \frac{\sin \theta + \tan \theta}{\csc \theta + \cot \theta} \cdot \frac{\csc \theta - \cot \theta}{\csc \theta - \cot \theta} =\\ \frac{\sin \theta \csc \theta + \tan\theta \csc \theta - \sin...
  41. K

    MHB Troubleshooting a Trigonometric Integral: Algebra and Solutions

    I have a few questions and a request for an explanation. I worked this problem for a quite a while last night. I posted it here. https://math.stackexchange.com/questions/3547225/help-with-trig-sub-integral/3547229#3547229 The original problem is in the top left. Sorry that the negative...
  42. opus

    Trig Equation — help to solve please: 0=cos^2(t)−t sin^2(t)

    I'd like to solve ##0 = \cos^2(t) - t\sin^2(t)## but it's been forever since I've done some trig and I'm real rusty. I've tried rewriting terms using identities such as ##\sin^2(t) = 1 - \cos^2(t)## but not getting anything helpful. Can I get a point in the right direction?
  43. Witcher

    Help for Trig or geometry? Where can i find the help?

    I am going over review to cover some trig fundamentals. Am stuck and am looking for the right place to get help for a question.
  44. A

    Partial Differential Equations result -- How to simplify trig series?

    Solve the boundary value problem Given u_{t}=u_{xx} u(0, t) = u(\pi ,t)=0 u(x, 0) = f(x) f(x)=\left\{\begin{matrix} x; 0 < x < \frac{\pi}{2}\\ \pi-x; \frac{\pi}{2} < x < \pi \end{matrix}\right. L is π - 0=π λ = α2 since 0 and -α lead to trivial solutions Let u = XT X{T}'={X}''T...
  45. M

    Will an algebra and trig texbook be sufficient preparation for calc?

    I took Algebra I, II, and precalculus in high school, but I graduated high school some time ago and would like to prepare for calculus before I go back to school. My question is if a textbook that covers both Algebra and Trigonometry will sufficiently prepare me for calculus (I plan on taking...
  46. M

    B Why do we care about trig identities?

    Homework Statement: This is not a homework question. I am trying to understand why we spend so much time studying trig identities. Homework Equations: As far as I understand, the two basic trig functions (sin and cos ) show the relationship between the sides of a right angle triangle in a...
  47. karush

    MHB How can I evaluate the integral using a trigonometric identity?

    Evaluate using a trig identity $$\displaystyle \int \dfrac{5}{x^2\sqrt{25-x^2}}\, dx$$ my first inclination to set $u=5\sin{x}$ then $du=5\cos{x}\, dx$ or $dx=\dfrac{du}{5\cos {x}}$
  48. V

    Finding the limit using a trig identity

    Find the limit as x approaches 0 of x2/(sin2x(9x)) I thought I could break it up into: limit as x approaches 0 ((x)(x))/((sinx)(sinx)(9x)). So that I could get: limx→0x/sinx ⋅ limx→0x/sinx ⋅ limx→01/9x. I would then get 1 ⋅ 1 ⋅ 1/0. Meaning it would not exist. However the solution is 1/81...