Trigonometry Definition and 664 Threads

I appreciate the opportunity afforded by this forum to submit a question. I have struggled with the derivation shown in the attached picture. I am certainly unfamiliar with the concept used to include the arctan function in the encircled step. Would be highly appreciative of a prompt.wirefree

For the triangle shown in the below image, ##\sin 60° = \frac{opposite}{hypotenuse} = \frac{y}{r}## ##\sin 30° = \frac{opposite}{hypotenuse} = \frac{x}{r}## The questions are: 1. What is the opposite and hypotenuse of sin 90°? 2. I am guessing that the opposite and hypotenuse of sin 90 is r...

I am in the 3rd grade of high school and we have a very weird math program.Since the school is specialised for economics we don't study trigonometry in the 3rd grade ,instead we learn about interest rates and how to calculate credits etc... Regardless, we have additional lections (which I am...

What do the functions cosx/x and tanx/x represent?

Homework Statement Prove that the ratios of the sides of a right angle triangle ( for example hypotenuse divided by ankathete...) are equivalent to the ratios of the congruent triangles. I believe this problem amounts to showing that sin(alpha)=sin(alpha') and the same for cosinus and tangens...

Alright. I am sort of understanding this section on my online math lesson, but I am still struggling with it. Would be gladly appreciated if someone could help me with this: If cosΘ = -4/9 with Θ in Quadrant II, find sinΘ

[Prefix] When we do trigonometric substitutions (such as for the integral x^3/(a^2-x^2)^2), we say something like "let x = asinp for -pi/2 <= p <= pi/2" then we carry on and solve the integral. However, sometimes our answer is ugly and we get some term in our expression like "cosp"- so we draw...

The problem a) find the length of AD in the figure b) Why are there two solutions in a) and what solution fits the figure? Figure The attempt I started with drawing a "help line" in the figure. The cosine formula for AC with respect to triangles ADC and CBA gives us two equations: ##...

What are some rigorous theoretical books on mathematics for each branch of it? I have devised a fantastic list of my own and would like to hear your sentiments too. Elementary Algebra: Gelfand's Algebra Gelfand's Functions & Graphs Burnside's Theory of Equations Euler's Analysis of the...

When we are given a problem to find the value of say tan(120 °), I was instructed to proceed by tan( 90*1 +30), which lies in the second quadrant and tan is negative in the second quadrant , plus odd multiple of 90 so it becomes -cot(30). Hence tan (90+α)= -cotα. But this works only because we...

How can I get a right triangle from the inputs and outputs of trigonometric functions? For example: sin(x) = y The triangle would have one angle as x and the opposite edge of the triangle would be y/hyp etc. How can I get all of these values from any trigonometric function? Please tell me if I...

I've developed a sort of aversion to doing huge calculations most of the time (at home) I just want to plug it into the calculator and do it . This is affecting my exams, I tend to put off questions which have a lot of calculation to do and then ultimately do the calculation wrong (We're not...

I'm currently writing my EP on various physical equations including Maxwell's equations, and I had to justify using the dot product of the normal unit vector and the electric field in the integral version. However, I can't think of a reason for not using trigonometry as opposed to the...

Prove \cos20^\circ\cdot\cos40^\circ\cdot\cos80^\circ=\frac18

The Attempt at a Solution I'm not sure where to start and the book doesn't show a 90 degree angle on the lower region where h meets the base. Can someone nudge me in the right direction please?[/B]

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...

Hi I'm looking for 2 books 1. a big geometry and trigonometry book that covers almost everything (also proofs) from basic to intermediate so i have a solid understanding of geometry trigonometry. 2. a geometry or trigonometry that gives you an appreciation for trigonometry fx how it was used...

I only memorized these trigonometric differential identities : `sin(x) = cos(x) `cos(x) = -sin(x) because I can convert tan(x) to sin(x) / cos(x) and sec(x) to 1 / cos(x) .. etcAnd there is no need to memorize some integral identities such as : ∫ sin(x) dx = -cos(x) + C ∫...

Solve $\large 3^{3\cos x(1+\sin^2 x)}-3^{\cos x(4-\sin^2 x)}=6\cos 3x$.

My calc. 2 book more or less only mentioned the hyperbolic functions to make integration easier, so, now that I have some free time, I'd like to explore the area further. Could someone recommend a good book on the subject or do I need to take more math first? A quick google search revealed...

Physics First, instead of the typically required Earth Science and Biology - Good idea, but for which students? For everybody, or just for those with enough Algebra and Trigonometry qualifications? http://en.wikipedia.org/wiki/Leon_M._Lederman

Simple question, but I can't figure it out. Consider an isosceles triangle ABC with \alpha=\beta dissected by a line through C and D, where D is on AB. It is obvious that |CD|<=|AC|=|BC|, but I want to prove it using trigonometry. I can use |BD|<=|BC| in my assumptions but not...

Homework Statement There is a part of solution of a question which says that: ##cot|cot^{-1}x|=cot cot^{-1}x=x## Homework EquationsThe Attempt at a Solution If we put ##x=-1## in this equation then ##cot^{-1}(-1)=-\pi /4## which will have a modulus =##\pi /4##. And ##cot \pi /4=1## which is...

Homework Statement [/B] Keep in mind this is a Top Gun-themed homework assignment. Cougar comes in for a shaky landing. His 20422 kg airplane traveling at 85 m/s strikes the deck at 3.5 degrees below the horizontal. Cougar's plane snags the landing cable stretched across the deck. The landing...

I know that ##\sin^2 x + cos^2 x = 1.## Is this mean that ##\sin^2 2x + \cos^2 2x = 1## or ##\sin^2 3x + \cos^2 3x = 1## or ##\sin^2 4x + \cos^2 4x = 1## and so on?

I'm trying to integrate a function in a classical physics problem but when I apply the limits it gave undefined results. Hence, I looked up that particular part of the solution and I did not fathom the function manipulation. It states that if x≤b in the following expression...

Prove that if $A,\,B$ and $C$ are angles of a triangle, then $\dfrac{1}{\sin A}+\dfrac{1}{\sin B}\ge \dfrac{8}{3+2\cos C}$.

Homework Statement See the document attached as it contains a diagram Homework Equations cos(theta) = adjacent/hypotenuse, sin(theta) = opposite/hypotenuse, tan(theta) = opposite/adjacent The Attempt at a Solution See document attached

1.A aircraft leaves base and travels west at a speed of 100km/hr for 25 minutes, then turns right and travels north at a speed of 25m/s for 1000 seconds, then turns right and travels east at a speed of 75 km/hr for 10 minutes. The plane is asked to return to base. Determine the direction that...

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...

Hey guys, The problem is #49 and it is a simple calculus problem, but the part that I am confused on is how the solution solves the trig. equation. In the solving, the solution brings out the plus-minus symbol and puts it outside the arccos, but I feel as if it should be inside the arccos. I...

Homework Statement The lines L1 and L2 with equations y=2x and 3y=x-1 respectively,are drawn on the same set of axes. Given that the scales are the same on both axes and that the angle L1 and L2 make with the positive x-asis are A and B respectively, write down the value of Tan A and the value...

Hello everyone. This is my first post on here. I figured that I would give it a shot. Just as a quick background: I'm studying electrical engineering and I'm working an internship for a machine manufacturing company now. One of the projects I have been assigned is to come up with a system to...

Assume that the Earth is spherical and recall that latitudes range from 0° at the Equator to 90° N at the North Pole. Consider Dubuque, Iowa (42.50° N latitude), and Guatemala City (14.62° N latitude). The two cities lie on approximately the same longitude. Do not neglect the curvature of the...

Let $P,\,Q,\,R$ be the angles of an acute-angled triangle. Prove that $\sin P+\sin Q> \cos P+\cos Q +\cos R$.

Homework Statement I am just stuck on a step in my problem , I have found the solution but have been attempting rearrange the equation but I just don't get it. Its probably a simple step Homework Equations 0=x[(tanα-tanθ)-(gx/2Vo^2Cos^2(α)] then this forms into this...

So I am a community college student and I would like to major in something within the stem field. When I arrived at cc in fall of 2014, I took my school's math placement test and scored into intermediate algebra. I wasnt satisfied with this so i went to my school's summer math academy and retook...

Solve the equation $\cos^k x-\sin^k x=1$, where $k$ is a given positive integer.

Homework Statement To prove that system will travel freely upto 180 degree m2 is counterweight and m1 is mass of pan (=3kg) i have attched the fbd or another link http://www.imagebam.com/image/54bb5a394377595 Homework Equations m1(h + a sin θ) g x = m2 y h g m2 = 9.13 kg The Attempt at a...

Homework Statement a boy on whom the force of gravity is 400 N hangs on to the middle of a rope stretched between two trees. The rope sags in such a way that it makes an angle of 170 degrees at the boys hands. what force does the rope exert on each tree? Homework Equations F=ma The Attempt at...

How many solutions does the equation $\sin a \sin (2a) \sin (3a) \cdots \sin (11a) \sin (12a) =0$ have in the interval $(0,\,\pi]$?

I'm making a model of a sine wave out of popsicle sticks. Essentially I'm digitizing a sine wave. Let's say I'm modeling half of a cycle with ten sticks. So I need to know how long to cut each stick. So I figured it would be cos(arcsin(x/10)) for x=0 through 9. Wrong! I still can't figure...

I think trig is assumed to be based upon triangles. This lumps trig next to squares, trapezoids, pentagons, hexagons, etc. Sure, triangles can be used to describe trig functions, but I think they do a disservice to your intuition. It's similar to Riemann sums versus integrals. True, integrals...

At first this sounds like a very popular and often asked/solved question but it has a twist - I need help with the twist please. 1. Homework Statement A cannon is at Point A in a 3d environment. There is a wall at Point B which sits between the cannon and a castle, at Point C. Write a...

Homework Statement So we have a force of unknown magnitude acting on these struts at an angle θ measured from strut AB. The component of the force acting along AB is 600lb, and the magnitude of the force acting along BC is 500lb. If Φ = 60°, what is the magnitude of F and the angle θ...

1) Question statement: Simplify 2sec^2x-2sec^2xsin^2x-sin^2x-cos^2x 2)Relevant equations: tan A=sinA/cos A 1+tan^2A=sec^A cot A=1/tanA cot A=cos A/sinA sin^2A+cos^2A=1 secA=1/cos A cosecA=1/sinA 1+cosec^2A= cot^2A sin2A=2sinAcosA cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1 tan2A=(2tanA)/1-tan^2A 3)...

1) Question: Show that (sin3A-sinA)/(cosA+cos3A)=tanA 2) Relevant equations: tan A=sinA/cos A 1+tan^2A=sec^A cot A=1/tanA cot A=cos A/sinA sin^2A+cos^2A=1 secA=1/cos A cosecA=1/sinA 1+cosec^2A= cot^2A sin2A=2sinAcosA cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1 tan2A=(2tanA)/1-tan^2A 3)Attempt...

Homework Statement For the following series ∑∞an determine if they are convergent or divergent. If convergent find the sum. (ii) ∑∞n=0 cos(θ)2n+sin(θ)2n[/B]Homework Equations geometric series, [/B]The Attempt at a Solution First I have to show that the equation is convergent. Both cos(θ)...

Homework Statement Solve for x 2sinx= 3x2 + 2x + 3[/B] Homework Equations Lowest value of quadratic function = -D/4a (D= Discriminant) The Attempt at a Solution I have no idea how to do it

Homework Statement sinӨ + cosӨ =4/3 ,, then sin2Ө = ... ? Homework Equations sin2Ө = 2cosӨsinӨ or any trigonometry functions... The Attempt at a Solution I tried to write sinӨ + cosӨ =4/3 in the form of cosӨsinӨ but couldn't.. is there a possible way to solve it ?