# Trig Definition and 35 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. ### Cars Collide on a Hill, Conservation of Momentum Help Please

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...
2. ### I Core of Euler's equation

Hi all: I really do not know what to ask here, so please be patient as I get a little too "spiritual" (for want of a better word). (This could be a stupid question...) I get this: eiθ=cosθ+isinθ And it is beautiful. I am struck by the fact that the trig functions manifest harmonic...
3. ### B Applications of Morley's Theorem

I was planning to do an essay exploring Morley's Trisector Theorem, but I was having trouble finding and real life applications of it? It states that "in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle". I thought it was pretty...
4. ### Trig problem involving a triangle's angles and sides

Homework Statement In the triangle ABC, angle A = 30 deg, angle B = 45 deg and since AC = a. The perpendicular from C on AB cuts AB in E. In this task you should calculate exact values. a) Determine AE, BC and AB expressed by a. b) Perpendicular from B on AC intersects the extension of AC in...
5. ### Hairy trig integral

<Moderator's note: Moved from a technical forum and thus no template.> where a, b, c, d and n, all are positive integers. Find the value of 'c'. ------------------------------- I don't really have a good approach for this one. I just made a substitution u = sinx + cosx I couldn't clear up...
6. ### B Using trig to find distance?

Hi there! I haven't yet taken a trigonometry course (I'm in High-school), but I have an amateur interest in surveying. Recently I began thinking about how I could calculate the height of a point relative to me, or the distance of the object from me. Naturally, I immediately thought of the...
7. ### Can you solve this triangle?

Homework Statement Completely solve this triangle. No calculators please. A=? B=Pi/3 C=? a=(1+sqrt(3)) b=? c=2 Homework Equations Cosine law: b^2=a^2c^2-2ac(cos(B)) Sine law: Sin(A)/a=Sin(B)/b The Attempt at a Solution b^2=-6 You can plug in 1/2 in (cos(B)) right away. Other attemps, don't ask...
8. J

### Geometry: Solve for angles of a triangle w/line intersecting

My mother's boyfriend's son who is in 6th grade asked me a question about the math they are learning. I thought it wouldn't be too bad but I cannot for the life of me figure it out. A solution would be greatly appreciated. 1. Homework Statement https://postimg.org/image/1tsa4v4t8r/ Homework...
9. ### Courses Calculus 3 -- looking for ways to help me understand

So I am in calculus 3 this year and have passed both calc 1 and 2 with a B and C+ respectively. I could have gotten a better grade but was lazy. I was lazy by using calculators and not actually learning the arithmetic and algebra. Now one serious issue I have is Trig. I can never remember trig...
10. B

### Help (: adding vectors! components.... angles, drawing.

Homework Statement A ship traveling 55 degrees [W of N] is 65km farther north after 3.0h. What is the ship's velocity. Homework Equations sin, cos, tan? The Attempt at a Solution I know that Vground= Vair + Vwind, and that Vground = Vboat + Vcurrent, but I'm not sure if that is even relevant...
11. ### Reduction Formulae Question : In= ∫x(cos^n(x))

Homework Statement Let In = ∫x(cos^n(x)) with limits between x=π/2, x=0 for n≥0 i) Show that nIn=(n-1)In-2 -n^-1 for n≥2 ii) Find the exact value of I3 Homework Equations ∫u'v = uv-∫uv' is what I use for these questions The Attempt at a Solution Rewritten as ∫ xcos^n-1(x) cosx u'=cosx...
12. ### Need help solving this trig equation

Homework Statement what's the best way to solve this equation: 3cos(θ) + 1.595*sin(θ) = 3.114 Homework Equations (sinθ)^2 + (cosθ)^2 = 1 The Attempt at a Solution I tried using the identity above to solve this equation and ended up with cosθ = +/- 1.0526.
13. ### [Calc] First max and min values of an underdamped oscillation

Homework Statement Determine the FIRST maximum and minimum values of the underdamped oscillation: y=e^(-x/2)(4sin(3x)+3cos(3x)) cm Homework Equations 3. The Attempt at a Solution [/B] I firstly differentiated the above equation and got: (-e^(-x/2)(22sin(3x)-21cos(3x)))/2 I checked this and...
14. ### Rounding error making my graphics barely off?

I'm trying to draw a circle and a (possibly rotated) square on a grid. I have the circle part down and it's the square that is giving me trouble. I am originally given 2 points which represent the coordinates containing opposite ends of the square. For example, those 2 points would be (8,14) and...
15. ### Solve acos²θ+bsinθ+c=0 for all values 0≤θ≤360°

Homework Statement Solve acos²θ+bsinθ+c=0 for all values 0≤θ≤360° a=16 b=6 c=-12 So 16cos²θ+6sinθ-12=0 Homework Equations Cos²x=1-Sin²x The Attempt at a Solution Identity: Cos²x=1-Sin²x 16(1-Sin²θ)+6Sinθ-12=0 16-16Sin²θ+6Sinθ-12=0 6Sinθ-16Sin²θ=12-16=-4 Divide by 2(?) 3Sinθ-8Sin²θ=-2...
16. ### Very quick easy Trig/Angle question

Homework Statement The river flows 5km/hr in the west direction. The boat that has a speed of 10km/hr. It starts from the south bank to the north. Then the question is to essentially find the angle theta. Homework Equations Tan-1(5/10) or Tan-1(10/5) The Attempt at a Solution Tan^-1(5/10)...
17. ### Explaining the Sine Formula to Acoustics Students

I'm (a music academic) teaching a musical acoustics course to a very mixed group (music students, science students, and neither). Today, I covered the basic concept of simple harmonic motion and how this produces a sine wave pattern of motion over time. In the extra time we had left over, I...
18. ### B Finding the smallest positive solution to trig equation

I have the equation ##\sin 3x = \cos 7x##, and, in degrees, I have to find the smallest positive solution. Immediately, we can see that sin and cos are equal if their arguments are complements, so ##3x + 7x = 90##, which means that ##x = 9##. I know that that is a correct solution, but how do...
19. ### Trig function help

Homework Statement Let C=cosx. Write sec(2x)csc(x)sin(2x) as a function of C. The Attempt at a Solution Am I on the right track 1/cos(2x) * 1/sin(x) * 2sin(x)cos(x) 1/(cos^2(x)-sin^2(x)) * `1/(sqrt(1-cos^2(x)) * 2(sqrt(1-cos^2(x))cos(x) What would i do from here?
20. ### Trig help with radians

Homework Statement Find all numbers x ∈ [0, 2π] satisfying tan x = cos x. Your answers should be expressed in radians, rounded to 4 decimal places. Show all your working. [You will need to use a scientific calculator that has buttons such as sin−1 or arcsin so as to be able to find the angles...
21. ### A Basic Spectral Analysis proof help

I'm reading "Time Series Analysis and Its Applications with R examples", 3rd edition, by Shumway and Stoffer, and I don't really understand a proof. This is not for homework, just my own edification. It goes like this: Σt=1n cos2(2πtj/n) = ¼ ∑t=1n (e2πitj/n - e2πitj/n)2 = ¼∑t=1ne4πtj/n + 1 + 1...
22. ### How to go from a*cosx + b*sinx TO A*cos(wt - phi)?

Moved from non-homework forum section, so homework template is not present. Express Cos(t - pi/8) + Sin(t - pi/8) in the form A*Cos(wt - phi). I got sqrt(2)*Cos(t-3pi/4). Not sure if that's right though
23. ### Trig integration

Homework Statement ∫sin(2sinh(3x)) Homework Equations The Attempt at a Solution okay so i did a u substitution letting u=3x so we get 1/3∫sin(2sinh(u)) but i have no idea how to get rid of the sinh, i tried writing in exponential form or maybe i have to use some identity.. I am not sure...
24. ### Calc BC derivative problem with trig and double angle -- Help please

Homework Statement Find f'(x) if f(x) = 8^(sin^2(3x)) Hint: you will need to use the double angle formula for trig functions and your answer should only have one trig function in it. Homework Equations if y=a^u then y' = ln a * a^u * du sin(2x) = 2sinxcosx The Attempt at a Solution We're...
25. ### Finding the coordinate of a point by Law of Cosines/Sines

Homework Statement A model for the suspension of a vehicle is shown where the spring has stiffness k = 178 N.mm and an unstretched length of 347 mm. Here is the picture: http://i.imgur.com/1dTVs12.jpg Part a asked to determine the value of P and the force supported by member AB so that the...
26. ### Geometry Beginning Trigonometry textbook

Good morning everyone, I have written a free math textbook, and I'd appreciate some feedback on it. It's about the basics of Trigonometry, including sine, cosine, tangent, radians, the unit circle, a bit on identities, and the Law of Sines, Cosines, and Tangents. I wrote it in a rigorous...
27. ### Find side length using trig

Homework Statement $AB = 20 cm$, $m∠A = 30°$ , and $m∠C = 45°$ . Express the number of centimeters in the length of $BC$ in simplest radical form. Homework Equations $sin A = sin C$ The Attempt at a Solution $AB = 20, BC = x$ D is the point where this obtuse triangle separates into 2 right...
28. ### Produce Standing Wave Problem

Homework Statement The equation of a transverse wave traveling in a string is given by y(x,t) = 10 cos (π/2)(0.0050x - 8.0t + 0.57), in which x and y are expressed in centimeters and t in seconds. Write down the equation of a wave which, when added to the given one, would produce standing...
29. ### Algebra Algebra 2 and Trig textbooks

Hey PF, as my thread a week or two ago said I am currently planning on taking a college Calc and Analytic Geometry class with formal education only up to Geometry. I am very proficient in Geometry, good in algebra 1, have some experience in Trig and a little in Algebra 2. For this reason I was...
30. ### I'm having trouble creating my own trig function

I'm developing my own trigonometric function concerning a "real world" problem of my choosing. I decided to go with the orbit of Neptune around the sun. I just don't know how to develop the equation itself, like if it would be sine or cosine? I'm just lost as to where to begin. If anyone can...
31. ### I need to figure this out: (A×B)⋅C

Homework Statement Calculate (A×B)⋅C for the three vectors A with magnitude A = 5.00 and angle θA = 25.1∘ measured in the sense from the +x - axis toward the +y - axis, B with B = 4.18 and θB = 62.0∘, and C with magnitude C = 5.82 and in the +z - direction. Vectors A and B are in the xy-plane...
32. ### Trig, how long is the graph under y=0

Homework Statement f(x)=20+25*sin(0.85x) x = number of hours from start. f(x) = temperature. For how long is the temperature negative (under 0) during the first 10 hours? We haven't learned how to derive/integrate trig equations so that is out of the question. Homework Equations The Attempt...
33. ### Relative motion help please

Homework Statement A ships captain wishes to sail his ship north -east. A current is moving his ship with a velocity of 5.0km/h . If the ship has a maximum speed of 30 km/h what is the ships required heading? Homework Equations Cos angle=A/H The Attempt at a Solution Heading=cosine (5/30)...
34. ### 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 :) :)
35. ### Best angle to shoot a projectile

Homework Statement A projectile is fired with speed v_0 (velocity subscript zero) at an angle θ from the horizontal as shown in the figure Consider your advice to an artillery officer who has the following problem. From his current position, he must shoot over a hill of height H at a target...