What is Trig: Definition and 1000 Discussions

Homework Statement http://imgur.com/a/emr1n ∫01 x= 4tan(pi*y/4) , Find the volume of the solid by revolving shaded region about the y-axis Homework Equations tan^2=sec^2 - 1 The Attempt at a Solution I ended up with 64-16pi using u-substitution, not sure if right, want a confirmation. I only...

Homework Statement Homework Equations none The Attempt at a Solution [/B] I literally just posted this in the thread: https://www.physicsforums.com/threads/proving-identities.881951/ But since it was marked solved I doubt anyone will see it. So sorry in advance for making a new thread on...

Homework Statement Homework Equations none The Attempt at a Solution Two possible locations on the coordinate axis for the terminal arm of angle A: Two possible values for the measure of angle A and the related acute angle: Can someone please tell me if I did this correctly?

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...

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?

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...

$\large{S6.7.R.27}$ $$\displaystyle I=\int_{0}^{\pi/2}\cos^3\left({x}\right)\sin\left({2x}\right) \,dx = \frac{2}{5}$$ since $\sin\left({2x}\right)=2\sin\left({x}\right)\cos\left({x}\right) $ then.. $$I=2\int_{0}^{\pi/2}\cos^4\left({x}\right)\sin\left({x}\right)\, dx \\ \begin{align}...

$\large {S6.7.1.17}$ $\tiny\text {trig Integration}$ $$\displaystyle I= \int x \sec\left({x}\right)\tan\left({x}\right)\, dx \\$$ OK this has 3 terms so the inclination is IBP If $u=\tan\left({x}\right)$ and $du=\sec^2 \left({x}\right) \, dx $ but don't see this fitting in $\tiny\text{...

I have this integral: $$\int_{}^{}\frac{1}{x^2 - 9} \,dx$$ I believe I can use trig substitution with this so I can set $x = 3 sec\theta$ Evaluating this, I get $$ln|\csc\left({\theta}\right) - \cot\left({\theta}\right)| + C$$ Since $x^2 - 9 = 9sec^2\theta - 9$, then $\frac{x^2 - 9}{3} =...

I have the expression $$\sqrt{ a ^2 - x^2}$$ using trig substitution (with $x = asin\theta$), I get$$\sqrt{ a ^2 - a^2sin^2\theta}$$ which gets simplified to $ a \sqrt{ cos^2\theta}$ and then $ a cos \theta$ for $$- \frac{\pi}{2} \le 0 \le \frac{\pi}{2} $$ what I don't get is domain of...

[mentor note] moved to homework forum hence no template. HI, I'm just having a bit of trouble with the numerator part of this identity ... Resolving the the denominator is fairly straightforward but .. Can anyone shed light on the final couple of steps (sin^3 x - cos^3 x)/(sinx + cosx) =...

Whit 8.7.23} trig u subs s87.3 nmh{1000} $\displaystyle I=\displaystyle\int {\sin^3\left({t}\right) \cos^4\left({t}\right)} \ d{t} =\int\ (1-\cos^2\left({t}\right)) \cos^4\left({t}\right) \sin\left({t}\right) \ dt \\ \begin{align}\displaystyle u& = \cos\left({t}\right)&...

$\tiny{8.7.16}$ $$\int{t}^{3}\sqrt{1+{t}^{2}} \ dr =\frac{\left({t}^{2}+1\right)^{5/2}}{5} -\frac{\left({t}^{2}+1\right)^{3/2}}{3}+C$$ $$t=\tan\left({u}\right) \ \ \ dt=\sec^2\left({u}\right) \ du $$ Substituting $$\int\tan^3\left({u}\right)\sec^3\left({u}\right) \ du $$ Which doesn't...

mnt{7.3} nmh{2000} $$\displaystyle \int\frac{1}{{t}^{2}\sqrt{1+{t}^{2}}} \ dt = \frac{-\sqrt{t^2+1}}{t}+C$$ $\displaystyle t=\tan\left({u}\right)$ $\displaystyle dt=\sec^2(u) \ du $ $$\int\frac{\sec^2\left({u}\right)} {\tan^2\left({u}\right)sec\left({u}\right)} \ du...

$\tiny\text{Whitman 8.7.12 trig integral} $ $$\int\cos^4\left({t}\right) \ dt =\frac{3t}{8} +\frac{\sin\left({2t}\right)}{4 } +\frac{\sin\left({4t}\right)}{32} +C$$ Didn't know how to break this up in that the answer has 3 terms + C $\tiny\text {from Surf the Nations math study group} \\...

What is the adjacent side to an angle at 90 degrees? Aren't two sides adjacent to it?

Homework Statement A loading ramp is 2.8m long. One end rests on a loading dock 0.7 meters above the ground, and the other end leads into the back of a a tractor trailer 1.2m above the ground. Find the horizontal distance between the back of the truck and the loading dock, to the nearest tenth...

{8.7.4 whit} nmh{962} $$\displaystyle I=\int \sin\left({t}\right) \cos\left({2t}\right) \ dt $$ substitution $u=\cos\left({t}\right) \ \ \ du=-\sin\left({t}\right) \ dt \ \ \ \cos\left({2t}\right) =2\cos^2 \left({t}\right)-1 $ $\displaystyle I=\int \left(1-2u^2 \right) du \implies...

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...

Whitman 8.4.8 Trig substitution? Whitman 8.4.8 Complete the square.. \begin{align*} \int\sqrt{x^{2}-2x}dx &=\int\sqrt{x^{2}-2x+1-1}dx\\ &=\int\sqrt{(x-1)^{2}-1^{2}}dx\\ &=\int\sqrt{U^{2}-1^{2}}dx\\ \end{align*} Was wondering what substation best to use...

Homework Statement Express $$ 2 arctan (\sqrt\frac{a-b}{a+b} tan (\theta/2))$$ in terms of inverse cosine Homework Equations I realize it amounts to find a smart substitution, but I can't find one. The Attempt at a Solution I tried ##b/a=tan \theta## , but I can't find any way to get rid of...

Say I have the integral of [ 1 / ( sqrt( 1 - x^2) ] * dx . Now I was told by many people in videos that I substitute x = sin theta, and this has me confused. Wouldn't I need to substitute x = cos theta instead? as x = cos theta on the unit circle instead of sin theta? Thanks in advance for...

Homework Statement Solution set of the inequality (cot-1(x))2 -(5 cot-1(x)) +6 >0 is? Homework EquationsThe Attempt at a Solution Subs cot-1(x)=y We get a quadratic inequality in y. y2-5y+6>0 (y-2)(y-3)>0 Using the wavy curve method, the solution set is...

I am planning on doing a huge self-studying over geometry and hopefully a little bit a trigonometry session over the summer at my public library. Over at a friends house, I see that he has a book about "algebra 2 for dummies" in his pile of science books and it got me wondering, are the "For...

Well, are there? I thought that problems involving the verification of identities pretty much checked themselves because you know whether the steps you’re doing are legitimate or not and, of course, you know whether you’ve reached the expression you want. However, I got one of these problems...

Homework Statement [/B]Q7 part a on one of the attached pictures 2. Homework Equations Trigonometric identities The Attempt at a Solution See attached pages Please help me I've spent onwards of 4 hours trying to figure this out and I can't get anywhere at all

so basically I have been trying to add into a car and circuit simulation wind speed and direction, now I was thinking that cos degrees would work fine, so "wind direction - driving direction = affective direction." This works for head wind -1 and back wind 1 as well as side winds, 0 (no affect)...

My daughter is a Sophmore in high school and is taking Calculus with a current focus on Trig. I am trying to help her study but this stuff is way over my head...but I am trying! Can anyone help me with this? Here are a few of her study problems that we cannot figure out. Can you help me to...

Homework Statement Find the domain of this function and check with your graphing calculator: f(x)=(1+cosx)/(1-cos2x) Homework EquationsThe Attempt at a Solution i get to (1+cosx)/(1+cosx)(1-cosx) which is factored. so then setting each one to zero one at a time i figure out that cosx = -1 and...

On the paper I'm reading the arctan of 35 over 65 is approx. 28.30degrees. When I use the Google calculator "arctan(35/65)" gives me 0.493941369 rad. What am I doing wrong?

1. The problem is as follows: ∫(√1+x^2)dx/(x) 2. Using trig sub --> x = atanΘ with a = √1 = 1. So x = tanΘ and dx = sec^2ΘdΘ. 3. Picture included of attempted solution. I tried u substitution with both u = secΘ and u=tanΘ but didn't have the right du...

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

Homework Statement The problem is the integral attached Homework Equations sec2(u)=(1+tan2(x)) a2+b2=c2 ∫cos(u)=-sin(u)+C The Attempt at a Solution The solution is attached. I am wondering if someone could give me a hint where I went drastically wrong or where I possibly dropped a negative...

May someone kindly assist me to prove this trig identity (Sin2x-tanx) / cos2x = tanx Thank you for your assistance

When creating a right triangle in a unit circle how do you know where to place the leg from the terminal side? My textbook and Khan academy don't really explain this and it's just sort of assumed that I'd know. For example, If theta is equal to 135 degrees, where does the leg to complete the...

I have re-post this forum as I should have paid closer attention to rules. I apologized for that. Homework Statement 1) The expression tan^3 θ + sinθ/cosθ is equal to: (a) cot θ (b) tan θ sec^2 θ (c) tan θ (d) sin θ tan θ (e) tan θ csc^2 θ 2) Simplify (cos θ/1+ sin θ - cosθ/sinθ-1)^-1 (a)...

If $\sin\left({\theta}\right)=\frac{\left(p-q\right)}{\left(p+q\right)}$ And $p$ and $q$ are $90^o<\theta<180^o$ and $p>q$ Show that $\tan\left({\theta}\right)=\frac{q-p}{2\sqrt{qp}}$ I tried using $q=\frac{2\pi}{3 }$ and $p=\frac{5\pi}{6}$ But not... To do this but theory I'm clueless

https://www.physicsforums.com/attachments/5246 I'm trying to follow this example but where does the $\frac{1} {2 } $ come from in step 3

Homework Statement ∫sin(2sinh(3x)) Homework EquationsThe 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 where...

I was wondering if you could do a trig substitution with cosine instead of sine. All the textbooks I have referred to use a sine substitution and leave no mention as to why cosine substitution was not used. It seemed that it should work just the same, until I tried it for the following Fint...

$$\int_{-1}^{1}\sin^7\left({x}\right) \,dx$$ From the graph of this it's apparent the answer is 0 But step wise. I did this $$\int_{-1}^{1}(\sin^2\left({x}\right) )^3\sin\left({x}\right)\,dx$$ With $$\d{}{x}\left(\cos^2\left(x\right)-1\right)=2\sin\left({x}\right)\cos\left({x}\right)$$...

$$\int_{0 }^{\pi/2 } x\sec^2 \left({{x}^{2}}\right)\tan\left({{x}^{2}}\right)\,dx$$ Not sure where to start on this... Except that $$\d{}{x}\sec^{2 } \left({x^2 }\right)=\frac{4x\sin\left({{x}^{2}}\right)}{\cos^{3}\left({{x}^{2}}\right)}$$

\arcsin\sin\left(\frac{11\pi}{5}\right) How do you simplify this?

Homework Statement The block resting on the inclined plane shown has a mass of 40kg. Determine the maximum and minimum value of P for which the block is in equilibrium. (fs=0.35 and θ=25°) The image on top is the diagram in the book and the image below it is my free-body diagram (not too sure...

Homework Statement Homework Equations The Attempt at a Solution Note: by real solution I mean the correct implicit derivative, not an actual real solution... Please help![/B]

I'm trying to understand how the derivative of this function: x=ρcosθ Becomes this: dx=−ρsinθdθ+cosθdρ First off I'm guessing that x is a function of both ρ AND cosθ, or else we wouldn't be using the product rule in the first place..Am I correct? So how could we write this in functional...

Hi, Can somebody please point me into a direction how to solve the attached trig problem? First step, where can I find such values for sin (alpha)?Thanks.

Homework Statement Given the differential equation (\sin x)y'' + xy' + (x - \frac{1}{2})y = 0 a) Determine all the regular singular points of the equation b) Determine the indicial equation corresponding to each regular point c) Determine the form of the two linearly independent solutions...

Hello! I was wondering if anyone could expand upon and help me with this as I'm struggling "Use continuity to evalute \lim_{{x}\to{\pi}}\cos(x+\sin(x))" I do remember faintly how to do limits of "normal" numbers, but with trig I did not learn at all so I'm confused. This is same as finding the...

I'm realizing now how much I need to know the exact values of various trigonometric functions, as shown in various trig tables. Memorizing is pretty arduous, and I'd prefer to understand it, so how can I learn all of these?