What is Trig: Definition and 1000 Discussions

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...

Homework Statement Prove that the roots of trigonometric polynomials with integer coefficients are denumerable. Homework EquationsThe Attempt at a Solution The book does not define what a trig polynomial is, but I am assuming it is something of the form ##\displaystyle a_0 + \sum^N_{n=1}a_n...

$$\iint_\limits{R}(3x^5-y^2\sin{y}+5) \,dA$$ $$R=[(x,y)|x^2+y^2 \le 5]$$

Homework Statement Show that ##e^x = x## does not have any solutions, and show that ##\sec x = e^{-x^2}## has only one solution. Homework EquationsThe Attempt at a Solution Here is my proof of the first proposition: Since ##e^x## is concave up on ##\Bbb{R}##, it must lie above all of its...

I was wondering exactly what parts of trig I need to do to do well in Calc II. I took trig this past spring and aced it and I'm taking Calc I this semester. I'm not worried about this semester because I know my instructor won't use trig outside teaching us how to take the derivatives of the trig...

My screenshots show an attempt at a solution and the given solution path from the book, but I can't seem to figure it out.

Prove, that for any triangle: \[\sum_{\alpha \in \left \{ A,B,C \right \}}\frac{1}{1+\sin \frac{\alpha }{2}}\geq 2\]

Hi, I know this is baby/fetus/sperm/molecule math for all of you, but I'm 13 and trying to self study my way to physics. Anyway, I'm teaching myself pre calculus. Most of it is pretty easy, but I've been stuck on sum/difference identities. It seems clear, and I'm folliwing everything the...

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...

How do you do this one? I can't figure it out! (2 - 5cot x) / (2 + 5cos x) = (2sin x - 5cos x) / (2sin x + 5cos 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...

Homework Statement Hi I am trying to understand this http://math.stackexchange.com/questions/341406/how-do-i-obtain-the-laurent-series-for-fz-frac-1-cosz4-1-about-0 So the long division yields...

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...

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.

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...

∫x2√(3+2x-x2) dx Here's what I've already done: completed the square ∫x2√(4-(x-1)2) dx (x-1) = 2sinθ sinθ = (x-1)/2 x = 2sinθ+1 dx = 2cosθ dθ trig sub + pulled out constants 4∫(2sinθ+1)2√(1-sin2θ)cosθ dθ trig identity 4∫(2sinθ+1)2√(cos2θ)cosθ dθ 4∫(2sinθ+1)2(cos2θ)dθ expanded + trig...

Hello. Do you guys know if there is an identity related to this expression \cos(A+B)\cos(A+C) If so, can you help me how to derive it? I need it for the derivation of the formula from my circuits analysis course. Thanks.

Hello, My teacher gave me some trig identity homework and it has completely stumped me :confused:. Would be really grateful for some help, thanks! The question is; Solve the equation cos2(x) + sin(x) = sin2(x) for 0o<=x<=180o I wasn't sure how to enter the degree symbol so i added ^0.

Given a unit-hypotenuse triangle, how do we get the inverse sin/cos/tan equations? I'm trying to program a high-precision fixed-fraction model of the sun and Earth and I've forgotten how the equations are derived. I know there's differentiation and integration. And I'm stuck on how to express...

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...

$\tiny{242.7x.25}$ $\textsf{Find the derivative of y with respect to x}$ \begin{align*}\displaystyle y&=8\ln{x}+\sqrt{1-x^2}\arccos{x} \\ &=\frac{8}{x}+? \end{align*}

Homework Statement ∫8cos^3(2θ)sin(2θ)dθ Homework EquationsThe Attempt at a Solution rewrote the integral as: 8∫(1-sin^2(2θ))sin(2θ)cos(2θ)dθ u substitution with u=sin(2θ) du=2cos(2θ)dθ 4∫(1-u^2)u du= 4∫u-u^3 du 4(u^2/2-u^4/4)+C undo substitution and simplify 2sin^2(2θ)-sin^4(2θ)+C The book...

Prove the inequality: \[\left | \cos x \right |+ \left | \cos 2x \right |+\left | \cos 2^2x \right |+...+ \left | \cos 2^nx \right |\geq \frac{n}{2\sqrt{2}}\] - for any real x and any natural number, n.

Hi, I am working on an engineering problem and I have an equation which takes the following form: x = (A * cosα * sinθ) + (B * sinα * cosθ) Can this be further simplified? It almost looks like one of the sum-difference formulas you find in tables of trigonometric identities. I'm not to sure...

I've written it out and it seems impossible. I get -50(sin^2(alpha)) = 86.63 cos(alpha) sin(alpha) - 6.54. Where would I go from there?

Is this precalculus minus trig?

I need some help graphing this trig function. f(x)=4sin(3x-2) When Graphing, the points should be over 2 periods and 9 points. I have: -Amplitude: 4 -Period=(2\pi/3) -Range=[-4,4] I need help on: -Graphing the points over 2 periods and 9 periods (parent function and f(x)) -Table of 9...

I am planning to self-teach myself Trigonometry and all the other required fields before jumping into calculus. I have compiled a list of books that I have researched and would like your opinions and recommendations. Books: Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry...

$$\int_{}^{} \frac{1}{x\sqrt{x^2 + 16}} \,dx$$ I can set $x = 4 tan\theta$. Thus $dx = 4 sec^2 \theta d\theta$ So, plug this into the first equation: $$\int_{}^{} \frac{4 sec^2 \theta }{4 tan\theta \sqrt{16 tan^2\theta + 16}} \,d\theta$$ Then, $$\int_{}^{} \frac{ sec^2 \theta }{4 tan\theta...

Homework Statement What is the next radius outwards of this Apollonian gasket? R = radius of outer circle = 5 r1 = radius of largest inner circle = 3 r2 = radius of second largest inner circle = 1 a = unknown radius Homework Equations C = 2πr A = πr2 d = 2r The Attempt at a Solution Make a...

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...

$\tiny{Whitman \ 8.7.23}$ \begin{align} \displaystyle I&=\int \sin^3(t) \cos^2(t) \ d{t} \\ u&=\cos(t) \therefore du=-\sin(t) \, dt \\ \textit{substitute $\cos(t)=u$}&\\ I_u&=-\int (1-u^2) u^2 \, du=-\int(u^2-u^4) \, dt\\ \textit{integrate}&\\ &=-\left[\frac{u^3}{3}-\frac{u^5}{5}\right]...

Homework Statement Solve cotxcsc2x=2cotx Homework EquationsThe Attempt at a Solution cotx(csc2-2) cotx = 0 x = no solution x = sin-1(1/√2) or x = sin-1(-1/√2) I come up with the solutions x = { π/4, 3π/4, 5π/4, 7π/4} However the solutions are telling me that x can also be equal to π/2...

Homework Statement Solve sin2x + sinx =0 Homework EquationsThe Attempt at a Solution I first factor and get sinx(sinx + 1) = 0 sinx = 0 x = sin-1(0) x= 0 x= π-0 = π sinx = -1 x= sin-1(1) x= π/2 x = π + π/2 = 3π/2 x = { 0, π, 3π/2 } However when I look at the solution this is correct but...

Homework Statement Solve sin (x + pi/4) = √2 cos x Homework EquationsThe Attempt at a Solution sinx*cos(pi/4) + cosx*sin(pi/4) = √2 cos x √2/2 sinx + √2/2 cosx = √2 cos x not sure if I am on the right track? or where would I go from here? would I bring √2 cos x to the left side?

I have $$\int_{}^{} \frac{1}{\sqrt{1 - x^2}} \,dx$$ I can let $x = \sin\left({\theta}\right)$ then $dx = cos(\theta) d\theta$ then: $$\int_{}^{} \frac{cos(\theta) d\theta}{\sqrt{1 - (\sin\left({\theta}\right))^2}}$$ Using the trig identity $1 - sin^2\theta = cos^2\theta$, I can simplify...

I have $\frac{sec\theta}{tan\theta}$. How can I simplify it to get $\csc\left({\theta}\right)$ ?

Homework Statement Under #3 Homework Equations Trig identities The Attempt at a Solution The picture attached is my attempt. The square in the upper upper left is the problem and the one in the lower right is my solution. I'm seeing that I'm getting the wrong answer, but not how.

Homework Statement $$sinx - cosx = 1/3$$ solve for $$sin(2x)$$ Homework Equations $$sin^2x + cos^2x = 1$$ $$sin2x = 2cosxsinx$$ The Attempt at a Solution I think you can square both sides and get: $$sin^2x - cos^2x = 1/9$$ But how can I use this information to solve for sin2x? Is there a...

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) or...

Homework Statement The question states to find the primary trig ratios for (7π)/4 Homework EquationsThe Attempt at a Solution I got sin= (-√2)/2 cos=(√2)/2 tan= -1 csc= 2/(-√2) sec= 2/(√2) cot= -1 I got all of them correct except for csc and sec, and I am unsure why the solutions are telling...

Homework Statement I have a series of 12 values that I need to calculate the Theoretical Intensity, I, using the formula below. I have found values for all variables and their uncertainties, and have calculated the I value for each set using the formula. Now I need to calculate the...

Here is the question: This is the step I came to after taking the derivatives and doing some simplification: ^ I did the work myself on paper, I just couldn't type out the whole thing clearly so that anyone else can see what I'm referring too... so I used some online tool to show that...

Homework Statement \int_{}^{∞} \frac{1}{n^2 - 4} dn Homework Equations I'm trying to do this a way that it isn't usually done. Normally this is done with partial fractions. I'm trying to do it by using trig substitution using sine, which requires some algebraic manipulation. For some reason...

206.8.8.49 $a=0 \ \ b=12$ $\displaystyle I_{49}=\int_{a}^{b} \frac{dx}{\sqrt[]{144-x^2}} \, dx = \arcsin{\left[\frac{1}{12}\right]} \\$ $ \text{use identity} $ $\sin^2\theta+\cos^2\theta = 1 \Rightarrow 1-\cos^2\theta=\sin^2\theta \\$ $\text{x substituion} $ $\displaystyle...

Is it possible to factor a quadratic equation along the lines of asin^2x -bsin2x+c ? If so, how? The sin2x seems to be a problem since when expanded it becomes 2sinxcosx, but I'm wondering if it is possible, and how it would be done? Thanks in advance.

In triangle ABC, ∠ABC = 90◦ . A median is drawn from A meeting BC at M such that AM = 5. A second median is drawn from C meeting AB at N such that CN = 2√10. Determine the length of the longest side of triangle ABC I have no idea where to even start on this one

Homework Statement My calc class is having me review precalc(which I'm really rusty on...) 21. Find sin θ, sec θ, and cot θ if tan θ = 27 22. Find sin θ, cos θ, and sec θ if cot θ = 4. 23. Find cos 2θ if sin θ = 15 24. Find sin 2θ and cos 2θ if tan θ = √2 25. Find cos θ and tan θ if sin θ =...

Homework Statement Given the diagram below, showing the path of a geocentric satellite S flying over a ground station G, find an expression for the geocentric semi-angle ##\phi## in terms of ##\epsilon##, the radius of the Earth ##R_E##, and the height of the orbit ##h##. Homework Equations...

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...