# What is Trignometry: Definition and 30 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. ### B Multiple Rotating Signs on a Fence Gate -- Overlap Question

Hey Everyone, This is a little project of mine. I'm including a daigram of it - top view -> down. This is part of a larger system. Consider a fence gate made of poles. In my diagram Point "A" in blue is a non-moving vertical pole. Point "B" red is a pivot point for an arm containing all...
2. ### B A Simpler Way to Find the Shaded Area?

Consider the following scenario: Given that points ##M## and ##N## are the midpoints of their respective line segments, what would be the fastest way to determine what percentage of the squares total area is shaded purple? I managed to determine that the purple shaded area is ##5\text{%}##...
3. ### Basic Proportionality Theorem (Thales Theorem)

According to Basic proportionalit theorem if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides proportionaly. I can't figure a way out how to prove it. Here is an attempt. we know that AE/EB = AD/DC.
4. ### Torque about a pendulum's suspension point

Homework Statement In the figure attached, what is the torque about the pendulum's suspension point produced by the weight of the bob, given that the mass is 40 cm to the right of the suspension point, measured horizontally, and m=0.50kg? Homework Equations tau = rFsin (theta) or tau = lF...
5. ### B Can you deduce ##\tan(\theta) = \frac {df} {dx}## from this graph?

Could someone explain to me how from this graph you can deduce that ##\tan(\theta) = \frac {df} {dx}##. Thanks
6. ### I Can Complex Equations Break the Bounds of the Unit Circle?

Is doing the same thing repeatedly... Can I spin out of the unit circle with the solution to this equation: (a^2 + b^2) / (a * b - a / b) = (a / b + b / a) Extra Credit for a refutation. Hint: signal processing.
7. ### What Are the Solutions for cos(2x) + cos(x) = 0?

Homework Statement cos2x + cos x = 0 (0 <= x <= 360) Homework EquationsThe Attempt at a Solution cos2x + cos x = 0 2cos(3x)/2 cos(x)/2 = 0 3x/2 = 90 degrees x = 60 degrees x/2 = 90 x = 180 3x/2 = 270 x = 180 x/2 = 270 x = 540 (not qualified) is there any more possibility (answers) for x?
8. ### Schools Can I take College Algebra and Trig at the same time?

Hello everyone, After about 6 years I'm finally getting out of the military in May and start going to school full time starting in the fall. I want to do engineering, but I know I'm behind in math and am worried about starting calculus. I want to improve my math by taking both College Algebra...
9. ### Solving cos(θ)^x+sin(θ)^x=1 for x: How many real solutions exist?

Homework Statement cos(θ)^x+sin(θ)^x=1 find the number of real values of x satisfying this equationHomework Equations noneThe Attempt at a Solution the answer given is 1 which is 2.which is obvious but i don't know how to prove that it is the only solution available
10. ### B Solve for x: Trigonometry Equation

While solving a problem I arrived at this equation: sin(x) / ( A - cos(x) ) = B A and B are known values. Is it possible to get x?
11. ### Draw the graph of arctan((x-1)/(x+1))

I am so far able to find the domain, intercepts, concavity and increase/decrease. But I am stuck at finding the asymptotes for the graph. I think there is no vertical asymptote or is there one at x=-1? I think the horizontal asymptote is y=pi/4
12. ### Solutions to Cos 2x Homework: 32 Answers

Homework Statement Cos 2x =√3/2 Find number of solutions .x∈[0,8π] Homework EquationsThe Attempt at a Solution :[/B] drew the graph of cos 2x.It has a periodicity of π and there are two solutions in each period. So 2*8 =16 solutions totally. But my teacher said that we must take [0,16π] as the...
13. ### How to tell when to use Cos vs sin in physics

Homework Statement The first problem was " A 50 N crate is pulled up a 5m inclined plan by a worker at constant velocity. If the plane is inclined at an angle of 37degrees to the horizontal and there exists a constant frictional force of 10N between the crate and the surface, what is the force...
14. ### Rutherford Scattering model geometry

Hi, I was just wondering if someone could help clarify how pi - theta = phi? That is the link to the youtube video I was watching, the guys pretty good check him out if you want to learn how to derive the differential scattering cross section.
15. ### Basic Trignometry: f(α).f(β) When α+β=5π/4

Homework Statement Let f(θ)=cotθ/1+cotθ and α+β=5π/4 then the value of f(α).f(β) is: The Attempt at a Solution f(α)f(β)= (cotα/1+cotα)* (cotβ/1+cotβ) = cotα.cotβ/((1+cotα)(1+cotβ)) =cotα.cotβ/(1+cotβ+cotα+cotα.cotβ)
16. ### MHB Katresha Davis' Trig Questions: Distance, Altitude & Ratio

Here are the questions: I have posted a link there to this topic so the OP can see my work.
17. ### Trignometry to non-right angled triangles?

I learned trignometry on the basis of right-angled triangles.Is it applicable to all(acute and obtuse) triangles?and how do you explian cos or sin(<=90),since it's no longer associated with right angled triangle?.can anyone please clarify.
18. ### Is 2a/sin 2x Equivalent to a Cot x?

Is 2a/sin 2x equivalent to a cot x?
19. ### How to solve Trignometry and Solution of Triangle questions

On my school days it was very simple because I used to take whatever I've and keep solving and by some or other ways I get succeed answering it but now as we are bounded by very less time (nearly a minute) so now I'm facing very hard time. How you know in which direction you need to go. I can't...
20. ### Trignometry Proof Help: Angle A < 60 Degrees

Trignometry Proof Help! If a,b,c are sides in a triangle such that a<1/2(b+c) show that angle A (the angle opposite to side a) is less than 60 degrees
21. ### How Are the Trigonometric Identities for Cosine and Sine Related?

Hi friends, Please make me understand this simplest function, y = cos θ 2. in the next step it says: cos θ = sin (π/2 - θ) 3. and similarly -cos (π/2 - θ) = -sin θ. Can anyone please explain how the steps 2 & 3 are deduced. Thanks, Nesta
22. ### How Do Trigonometric Functions Change with Shifts of π/2 and 2π?

Homework Statement Can you please list the formulae of function change while putting (pie/2 - x) and adding or subtracting 2Pie Basicly, I need help on 2 formulae. One is add/subtract Pie/2 and the other is add/subtract 2Pie. Homework Equations sin (pie/2 - x) = sin x cos (pie/2 - x) = - sin...
23. ### Trignometry Rules/properties/common equations?

Homework Statement What are the other Trignometry Rules/properties/common equations? The Attempt at a Solution cos2 theta + sin2 theta = 1 1 + tan2 theta = sec2 theta 1 + cot2 theta = csc2 theta 2sin theta = 2cos theta sin theta
24. ### Real life application of trignometry identities

Homework Statement Can anyone here help me find how and where trig identities are used in real life. can you also tell me which identity(with example) and is used for what purpose and how. Homework Equations The Attempt at a Solution I found out that it is used in the field...
25. ### Trignometry Inequalities in [0, 2pi)?

Homework Statement Solve the following equations or inequalities in the interval [0, 2pi). 2sin2x - 5sinx + 3 < 0 Homework Equations The Attempt at a Solution (2sin2x - 3)(sinx - 1) sinx = 3/2 or sinx = 1 Not sure what to do now sinx = 3/2 is impossible? sinx = 1...
26. ### Fundamental trignometry problem

how is trignometric ratios like sine theta is defined to be the ratio of perpendicular and hypotenuse in a right angled triangle?
27. ### How to Solve Complex Trigonometry Equations?

hi, i got 2 problems that are really hard to solve. i don't know wether they are trick question or they just can be incorperated in a formula.i have taken days to solve them but in vain. please help! a) 10(3^(2x+1)) = 2^(4x-3) b) (2/3x)^(log2) = (9x)^(log3) thanks you very much:-p
28. ### Solve Obtuse Trignometry Problems - Get a Headstart w/ Vijay

1) given that A is obstuse and that sinA=2/(sqaureroot of 5). find the value of cosA and tanA. 2)given that tanA=-5/12 and that tanA and cosA have opposite signs, find the values of sinA and of cosA. CAN SOMEONE TEACH ME EXACTLY HOW TO DO THESE PROBLEMS WITHOUT USING TRGNOMETRIC...
29. ### Help with grade 12 Trignometry project

Help with grade 12 Trignometry project!a.s.a.p pleasezz Hiii,, I am a grade 12 student ,and i have a math project related to sinosoidal functions to complete...My only problem at the moment is that ,with the notes my teacher gave to us it says that the sinosoidal regression on our calculators...
30. ### Solve Trigonometry Problem 0 <= Θ <= 180

Hi, I am doing A-Level maths P2 and am having trouble with solving this problems and others like it. Could you please tell me how to solve this and how to go about solving others lke these as when I look at the problem I have no idea how to start. The problem is the following: Solve for 0...