Trigonometry Definition and 664 Threads

In trigonometry equation (finding theta): 1) If the range of theta includes negative and positive part (such as -360<=theta<=360), and I got a value of 90,180,270 or 360.. Do I have to write the answer twice positive and negative? 2) if range of theta is positive only, and I got a negative...

I'm not stuck per say, but I need to know if I have the right idea for solving the rest of these questions. 1. Homework Statement For the following given trigonometric ratio and domain, determine the missing trigonometric ratio. Homework Equations cos\theta = -\frac{1}{2} ...

First I'd just like to point out that I'm taking calculus and advance pre-calculus simultaneously (kind of a stupid system) and this is a problem in the pre-calc. 1. Homework Statement 2. Homework Equations Let 'a' be arc length. a=\theta r a = \int_{a}^{b} \sqrt{1+[f'(x)]^{2}} dx...

Show that if $\dfrac{\cos x}{\cos y}+\dfrac{\sin x}{\sin y}=-1$, then $\dfrac{\cos^3 y}{\cos x}+\dfrac{\sin^3 y}{\sin x}=1$.

I've never really learned any trigonometry and I'm wondering if someone could tell me where I'm going wrong here. My reasoning is this: The hypotenuse of a 1,1,√2 right triangle is at a 45° angle to its base. Halving that angle should require that the base leg be doubled if the height leg is...

Problem was initially posted in a technical math section, so is missing the homework template. From a position 150 ft above the ground, an observer in a building measures angles of depression of 12° and 34° to the top and bottom, respectively, of a smaller building, as in the picture on the...

Homework Statement Homework Equations SinA/a = SinB/b = SinC/c The Attempt at a Solution a=38, c=44, ∠A = 35° What I have so far: sin(35)/38 = sinC/44 44sin(35) = 38sinC 44sin(35)/38 = sinC sinC = 0.6641 sin^-1(0.6641) ∠C = 41.6º Is this ∠C1? After this I don't know how to...

Why ##\sin (A+B) = \sin A \cos B + \cos A \sin B## and ##\cos (A+B) = \cos A \cos B - \sin A \sin B## ??

https://www.amazon.com/dp/1133949010/?tag=pfamazon01-20 https://www.amazon.com/dp/1285057090/?tag=pfamazon01-20 https://www.amazon.com/dp/1133959741/?tag=pfamazon01-20 So I'm planning on buying the books in the links above (Algebra and trig, precalc and calc by Ron Larson), but as they are...

Homework Statement [/B] Solve optimization problem; A person is to skate up a hockey rink, in a straight line(parallel to both of the sides), from wherever they are standing. They are to shoot the puck into the net whenever they reach the point where the angle on the net is the largest. Need to...

Hello, I asked for help on the "Science & Math Textbooks" subforum, but it looks like there are not many users in there. So I hope you don't mind if I ask for help in this subforum since I need help on this soon. Copy and paste from my other thread: "Hello, it has been a few years since I took...

Homework Statement A beam of polarized light of intensity 43.0 W/m2 is sent through a system of two polarizing sheets. Relative to the polarization direction of that incident light, the polarizing directions of the sheets are at angles θ for the first sheet and 90 degrees for the second...

Hello, it has been a few years since I took an algebra class, and therefore I have already forgotten a lot of material. I will be taking a college trigonometry class soon during winter session and I was wondering if you could recommend me a good Algebra I and II book to review before taking the...

Homework Statement sin ^{3}x + sin ^{3}(\frac{2\pi}{3} + x ) + sin ^{3}(\frac{4\pi}{3} + x) = \frac{-3sin3x}{4}Homework Equations sin 3x = 3sin 3x - 4sin^{3}x Mod note: The correct identity is ##sin(3x) = 3sin(x) - 4sin^3(x)## The OP realized this earlier but was unable to edit his/her post.The...

Homework Statement I'm trying to work out the period of a function of the form sin(ax)*cos(bx), where a =/= b. I'm trying solve how the values for a and b relate to the period. I've graphed a lot of functions, but I'm struggling to notice any patterns. The period always seems somewhat related...

Hi. Every time i read physics I feel so discouraged by my lack of understanding in terms of vector calculus and trigonometry. I do understand basic trigonometry and basic vectors but when professors or textbooks move onto combining derivatives with vectors i lack understanding of which rules...

Homework Statement Write down number 1+i and 1+i\sqrt{3} in trigonometry form.[/B]Homework Equations For complex number z=x+iy \rho=|z|=\sqrt{x^2+y^2} \varphi=arctg\frac{y}{x} And [/B]The Attempt at a Solution Ok. For z=1+i \rho=\sqrt{1+1}=\sqrt{2}...

Hi, i was just wondering since cosx=1-(x^2/2) is there a similar formatted formula for sinx?? much appreciated :) :)

Could someone credible please check my work on this one? Homework Statement This problem is "pulling a sled up a slope" All relevant data is in the picture. I wanted to find FP (The force one has to pull to start the sled moving up with slope). mass = 26.0kg μs = 0.096 slope of hill = 12...

Homework Statement "Calculate the following limit if it exists. If it does not exist, motivate why. \displaystyle\lim_{x\rightarrow 0} {\frac{x + x^2 +\sin(3x)}{tan(2x) + 3x}} Do not use l'Hôpital's rule." Homework Equations (1) \sin(a\pm b) = \cos(a)\sin(b)\pm\cos(b)\sin(a) (2)...

Homework Statement Does [sin(θ/2)-cos(θ/2)]^2 equal 1 for all values of θ? I need to figure this out to solve a physics problem. Homework Equations sin^2(A)+cos^2(A)=1 The Attempt at a Solution [sin(θ/2)-cos(θ/2)]^2 =sin^2(θ/2)+cos^2(θ/2) =1 But this isn't what I get when I put...

Evaluate $2\cos^3 \dfrac{\pi}{7}-\cos^2 \dfrac{\pi}{7}-\cos \dfrac{\pi}{7}$.

prove that $\tan\,6^{\circ}\tan\,42^{\circ}\tan\,66^{\circ}\tan\,78^{\circ} = 1$

Hi MHB, When I first saw the problem (Prove that $\sin^2 x<\sin x^2$ for $0\le x\le \sqrt{\dfrac{\pi}{2}}$), I could tell that is one very good problem, but, a good problem usually indicates it is also a very difficult problem and after a few trials using calculus + trigonometry method, I...

Solve the equation $\sin^7 x+\dfrac{1}{\sin^3 x}=\cos^7 x+\dfrac{1}{\cos^3 x}$.

Homework Statement Solve the equations sin(x+2y)=1/2 , cos(2x-y)=1/ sqrt(2) Homework Equations The Attempt at a Solution I tried getting a generic solution for both the first and second equation. How do I further proceed? By simultaneously solving? I so, how? 2x-y=2m*pi + or...

Find $m,\,n$ and $A$ such that $\sqrt{9-8\cos 40^{\circ}}=m+n\cos A^{\circ}$ where $m,\,n\in N$.

Hey guys, I have just a few more questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. I'm only asking about 1ab, ignore 2abc please: So for the first one, I used cos(30) as the estimated value to approximate L(28). Then I...

Hey guys, I have a couple of questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: For 1a, using inverse trigonometric derivative identities should work, right? I got y' = 1/sinØ + 1/cosØ and multiplied by the common...

This problem deals with finding the coefficient of friction between an object and a slope. It gives an object with mass m, sliding down a hill with a slope of θ at a constant velocity. I got mgsinθ=fksinθ. However the book shows mgsinθ=fk. The kinetic friction force and the force down the slope...

Find all values of $x$ which satisfy $\tan \left( x+\dfrac{\pi}{18}\right)\tan \left( x+\dfrac{\pi}{9}\right)\tan \left( x+\dfrac{\pi}{6}\right)=\tan x$.

please help me to solve these problems, 1. how many degrees, minutes, and seconds are respectively passed over in $11\frac{1}{9}$ minutes by the hour and minute hands of a watch? 2. The number of degrees in one acute angle of a right-angled triangle is equal to the number of grades in the...

What is the use of spherical trigonometry besides in navigation. My math background consist of having n completed a course in calculus 1. Would I ever need to learn and understand spherical trigonometry for further math or physics? What do I gain learning it besides saying I know spherical...

My problem is from Israel Gelfand's Trigonometry textbook. Page 9. Exercise 7: Two points, A and B, are given in the plane. Describe the set of points X such that AX^2+BX^2=AB^2. The attempt at a solution Since problem asked to describe set of points X such that AX^2+BX^2=AB^2, I tried to...

A rectangle with sides $x$ and $y$ is circumscribed by another rectangle of area $A^2$. Find all possible values of $A$ in terms of $x$ and $y$.

Homework Statement A circle with a radius (r) of 6000km. From the centre of the circle to a point in the distance G where another person is standing is R = 40000 km. Calculate the angle (θ) that the observer has to stand at point (O), to allow the observer to see the distant point G. If the...

Hi Guys, This is my second post relating to my problem, But I've boiled it down to more simple trig. sadly, I still can't figure it out. See the sketch below; what I want to obtain is x as a function of R. the angle in red, θ is the same for the two corners. What is known: 1) two...

Hi all, I've been looking and searching around for a good book for some pre-calculus review, and decided on one of Sheldon Axler's books. Looking at his site and the contents of both books (links below), I'm not sure what the difference is between them, other than some re-ordering of things...

Hi awesome people at physicsforum, I’m planning on doing some self-study in physics and math and I’d really appreciate some advice based on my skill -level and what I want to achieve, which I’ll describe for you. I’ve considered some books to buy further down, and would deeply appreciate...

On a trafo i just bought, it says COS Ø = 0,99. What does this mean? Is there some angle involved in changing the voltage?

Gents, Thanks for all the guidance in the past with my work and brothers too. Can anyone help with these , see file attached

Homework Statement Determine whether the series [3+cos(n)]/n from n=1 to infinity is convergent or divergent. Explain your reasoning and demonstrate that any conditions required to use a particular test are satisfied. Homework Equations Any series tests: ratio test, alternating sequence...

Evaluate: $$\frac{1}{\cos^210^{\circ}}+\frac{1}{\sin^220^{ \circ }}+\frac{1}{\sin^240^{\circ}}-\frac{1}{\cos^245^{\circ}}$$

We got a circle with a radius R. From a distance D from the centerpoint a line is inserted at an offset angle A1 from a line drawn though the centerpoint C of the circle, see the picture below. http://cdn.imghack.se/medium/0861cdab13b8957018f8e167342f2b8e.png I would like the are of...

Homework Statement Find the limit Homework Equations lim θ→ ∏/6 (sinθ - 1/2)/(θ - ∏/6) The Attempt at a Solution well, if you substitute the values, it gives 0/0, but that means that is undefined and that's not the answer. according to my book the answer is √(3)/2 and I am not supposed to...

Hello I have -csc^2 x Is this the same as -(cscx)^2 or (-csc x)^2? Thanks, Tim

Hi, I've looked under the mathematics textbook section on this site and I can see algebra and geometry but not a single trigonometry book... Is trigonometry normally covered in algebra books something? My trigonometry is really quite terrible and I know the absolute basics so I'm looking for...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Here is the question: I have posted a link there to this thread so the OP can see my work.

Hello, i'm doing some revision and working through the textbook my course follows and have a small problem. The question is an incomplete table of values for sinθ, cosθ, tanθ, \alpha and θ. I have to work out the blanks using what is given. I thought I knew the correct method of doing...