What is Trig: Definition and 1000 Discussions

Evaluate $$\int_0^{2\pi}\sqrt{\dfrac{1-\cos{x}}{2}}\,dx$$ ok my baby step is $$\int _0^{2\pi }\frac{\sqrt{1-\cos \left(x\right)}}{\sqrt{2}}dx$$ then ? W|A said the answer was 4

Ok I tried to follow an example but kinda got lost in this maybe more steps the answer is from W|A

Interpolating a straight line with a trigonometric function. In Matlab I ended up with this expression. fplot(@(x)(.0000001*cos(x*2*pi)+10), [0 1]) Would anyone like to discuss what this could be used in?

2tanx= 1/2tan2x 4tanx=2tanx / 1 - tan^2x 1- tan^2x = 2tanx / 4tanx tan^2x = 1/2 tanx = √1/2 Textbook answer 0 ; +/- 0.615 rad Not sure where I am going wrong.

I have a right triangle: one of the angles is ##60°## (that's ##\theta##), one of the sides is ##40 m## long, and the hypotenuse is equal to the radius. Now I can find an expression for ##r## and that expression is ##r=\frac{height}{sin \theta}##. If I differentiate it, I'll get ##\dot r## and...

Hello, I'm trying to solve the following equation : cos(x)=sin(x) + 1/\sqrt{3} in order to find cos(x)3 - sin3(x) = ? i tried to slove for sin(x) using sin2 + cos2 =1 replacing cos(x) by the first equation and i end up with a second degree polynomial using x = sin(x) and there are 2...

I am currently a community college student majoring in Computer Science, and I was placed into Calculus 1. I had to withdraw from this course for two semesters now. My professor advised me that I have "Algebra Issues". With my weaker foundation of Algebra, I plan to take the College Algebra...

$\begin{align*} \frac{\cot {x}-1}{\cot{x}+1}&=\frac{1-\sin 2x}{\cos 2x}\\ \frac{\cos {x}-\sin x}{\cos{x}+\sin x} \frac{\cos x-\sin x}{\cos x-\sin x}&= \\ \frac{\cos^2x-2\sin x\cos x+\cos^2 x}{\cos^2 x-\sin^2 x} \end{align*}$ so far..

Homework Statement Integrate: $$\int \frac{dx}{x^2\sqrt{4-x^2}}dx$$ Homework EquationsThe Attempt at a Solution I got to the final solution ##\int \frac{dx}{x^2\sqrt{4-x^2}}dx=-\frac{1}{4}cot(arcsin(\frac{1}{2}x))##. But It's the method where you transform that to the solution...

Homework Statement 1. A weight hangs from a spring. If a force is applied to the weight at t = 0 seconds, it will start moving up and down. The following equation gives the distance d, in centimetres, of the weight from its equilibrium point: d=4(sin5t-4cos6t) At what times during the...

The other day in a fit of boredom I decided to dust off my old math books (high school and undergrad) and see if I can still crank through the basics. 1. Homework Statement Show the following: $$ \frac { 3 cos^2(x) } { 2 - 2 sin(x) } = \frac { 3 }{ 2 } ( sin(x) + 1 ) $$ Homework Equations $$...

Basically the altitudes of a parallelogram have two lengths, 8 and 10 and they intersect at an angle whose sine is 1/4. I'm attempting to find the area of the parallelogram. I'm having trouble creating a good picture of it. Seeing if I could receive some help, thanks!

Homework Statement link: https://ibb.co/Xy9s6DR What is the magnitude of this force? Homework Equations Coulomb's Law Trig equations The Attempt at a Solution (.05 m)xcos(60)=0.025m (the distance between the two known charges) F(between the two known...

If I want to find the point where the graphs of ##y=cos^2(x)## and ##g=sin^2(x)## intersect, I would set the equations equal to each other and solve for the ##x##. This solution is ##x=sin^{-1}\left(\frac{\sqrt{2}}{2}\right)=\frac{π}{4}+2nπ,\frac{3π}{4}+2nπ##. However these the graphs do...

Homework Statement ##\int_0^{π/8}sin^2(x)cos^2(x)## Homework EquationsThe Attempt at a Solution Please see my attached work to see the train of thought. I've tried this thing about 100 times and still can't get the correct solution. I don't know if it's in the anti derivative evaluations of...

Hi all: I really do not know what to ask here, so please be patient as I get a little too "spiritual" (for want of a better word). (This could be a stupid question...) I get this: eiθ=cosθ+isinθ And it is beautiful. I am struck by the fact that the trig functions manifest harmonic...

I was planning to do an essay exploring Morley's Trisector Theorem, but I was having trouble finding and real life applications of it? It states that "in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle". I thought it was pretty...

I have the statement \sin[\sin^{-1}(x)] = x \hspace{7pt} if -1 \leq x \leq 1. How can I tell if plugging in x will return x for \cos[\cos^{-1}(x)] and \tan[\tan^{-1}(x)] ? What if the positions of the regular and inverse functions were reversed? For example, \cos^{-1}[\cos(x)]. I am only...

$\textsf{Evaluate the integral}$ $$I=\displaystyle\int\frac{x^2}{\sqrt{9-x^2}}$$ $\textit{from the common Integrals Table we have}$ $$\displaystyle I=\int\frac{u^2}{\sqrt{u^2-a^2}} \, du =\frac{u}{2}\sqrt{u^2-a^2}+\frac{a^2}{2} \ln\left|u+\sqrt{u^2-a^2}\right|+C$$...

Homework Statement In the triangle ABC, angle A = 30 deg, angle B = 45 deg and since AC = a. The perpendicular from C on AB cuts AB in E. In this task you should calculate exact values. a) Determine AE, BC and AB expressed by a. b) Perpendicular from B on AC intersects the extension of AC in...

Homework Statement I worked a physics problem and the answer came down to solving these two equations and I am stuck. Homework Equations [/B] 2 equations and two unknowns. sin(x) = (2/3)sin(y) 1 + cos(x) = (2/3) cos(y) The Attempt at a Solution I tried this and it went nowhere.. z...

Homework Statement This is an example worked out in the textbook Matter and Interactions, 4th Edition (pg. 181). The authors assume that solving for two unknowns is no problem, so they don’t show the steps. I’m trying to work it out and am stuck. I’ve used Alpha to get a step by step solution...

Homework Statement It's not a problem per se, I'm just trying something, so there's no statement. What I'm trying to do it's to prove the forllowing equation but without using the member of the right. (cos(36º) + 1)²/(cos(36º)) = 5cos(36º) There's the trivial answer, using both members, that...

Homework Statement A canoe is floating down a creek. The canoe is first spotted 80 feet away. 7 minutes later the canoe is 45 feet away, making a 40° angle between the two sightings. How far did the canoe travel? Homework Equations Law of Sines and Law of Cosines The Attempt at a Solution...

What does Tan (Theta - Pie) = ? I know Tan (theta + pie) = tan (theta). They say the answer is tan (theta), but I think it's some kind of typo.

How do I solve these? https://imgur.com/a/NvzxFcS

$$\displaystyle y^\prime +(1/x)y = 3\cos 2x, \quad x>0$$ first how do you get $u(x)$ from this

Homework Statement Simplify: $$sin^2\left(x\right)+sin^2\left(x\right)tan^2\left(x\right)$$ Homework Equations All trigonometric identities. The Attempt at a Solution (i) ##sin^2\left(x\right)+sin^2\left(x\right)tan^2\left(x\right)## (ii)...

Homework Statement Evaluate and express your answer in radians: $$cot^{-1}\left(1\right)$$ Homework EquationsThe Attempt at a Solution I start by identifying that the domain of Arccotangent is all real numbers. So 1 is in the domain. From here, I looked at the unit circle and saw that...

Given that √5 tanA=-2 and CosB=8/17 in ∆ABC State why we may assume that angle C is acute and determine the value of Sin CAttempt made: tanA=-2/√5 CosB=8/17 A is obtuse angle of 138° or reflex angle 318.19° B is an acute angle of61.9° or reflex angle298.1 °.Since it is a right...

i'm going back to school in September. I'm brushing up on my math knowledge/skills now and thinking of maybe joining a math club when i am back in school. I've often thought if i had an expert to talk to i could learn math a lot quicker than relying on just written instruction ... so maybe i...

Homework Statement Homework Equations 3. Solution Then the equations from part (A) are used--but why does the converted trig (1-cos(etc)) go away? Does this have to do with the mean-squared bit?

Homework Statement Back with more trig identities. Verify that the following is an identity ##-tan\frac{a}{2} = cot\left(a\right)-csc\left(a\right)## Homework Equations All pythagorean identities, double angle formulas, half angle formulas The Attempt at a Solution In the picture that I've...

Evaluate the trig expressions using the method shown in the textbook. Steps A through C show the method given in the textbook. 1. cos 4π/3 A. We are told to graph cos 4π/3. We are in Quadrant 3. B. Find the reference number r. r = 3π/2 - 4π/3 r = π/6 C. Evaluate r. cos π/6 = -sqrt{3}/2...

Evaluate the trig expressions using the method shown in the textbook. Steps A through C show the method given in the textbook. 1. sin 210° A. We are told to graph sin 210°. We are in Quadrant 3. B. Find the reference angle R. R = 270° - 210° R = 60° C. Evaluate sin R. sin 60° = -sqrt{3}/2...

Homework Statement Use the power reducing formulas to rewrite the expression that does not contain trigonometric functions of power greater than 1. Given expression: ##4sin^2xcos^2x## 2. Homework Equations Relevant Power-Reducing Formulas: ##sin^2x=\frac{1-cos2x}{2}##...

The following question, in my opinion, is not well-explained in Section 6.2 by David Cohen. I went over the question several times but it is not clear at all. Use the picture to approximate the following trig values to within successive tenths. Then use a calculator to check your answers...

How do I determine which trig value is bigger or smaller without using a calculator? Sample: Which is bigger: cos 2 or sin 2?

<Moderator's note: Moved from a technical forum and thus no template.> where a, b, c, d and n, all are positive integers. Find the value of 'c'. ------------------------------- I don't really have a good approach for this one. I just made a substitution u = sinx + cosx I couldn't clear up...

Homework Statement why this formula works ? Homework EquationsThe Attempt at a Solution when i take the derivative of the right side ,,, there is an additional "a" in the numerator in place of 1,, why the derivative of arcsine of (u/a) not exactly same with the expression under the integral sign

1. Here's the problem on trig integrating that I'm struggling with (Calculus 2 btw) 2. Wanted to see if I did everything right so far and what to do after all this. The part where I'm stuck is how to integrate (integral)cos^(2)udu and (integral)cos^(2)usin^(2)udu. I'm sure these are easy...

Hi there! I haven't yet taken a trigonometry course (I'm in High-school), but I have an amateur interest in surveying. Recently I began thinking about how I could calculate the height of a point relative to me, or the distance of the object from me. Naturally, I immediately thought of the...

Mod note: Moved from a Homework section, as this is more of a conceptual question than an actual homework problem. I can't really memorize the unit circle, but I do remember my instructor teaching us how to use reference angles to evaluate any trig function without needing the unit circle. I was...

Homework Statement solve xsin(x)-cos(x)=0 on interval (0,4) using the calculator Homework Equations xsin(x)-cos(x)=0 The Attempt at a Solution I have tried working the problem out through first pressing menu- 3 (algebra)- 1 (solve)- inserting the equation- inserting the interval. However...

Not a particular problem to wonder about but more of a general question, when one has a free body diagram, when is it best to use sine and when is it best to use cosine? I am reviewing some of my tests for a final, and having previously re-read my forces chapter, I thought that angles rising...

Homework Statement Completely solve this triangle. No calculators please. A=? B=Pi/3 C=? a=(1+sqrt(3)) b=? c=2 Homework Equations Cosine law: b^2=a^2c^2-2ac(cos(B)) Sine law: Sin(A)/a=Sin(B)/b The Attempt at a Solution b^2=-6 You can plug in 1/2 in (cos(B)) right away. Other attemps, don't ask...

Hello, I understand that solving an equation like f(x)=0 means finding those values of x that make the equality true. In the case of some difficult trig equations (like sin(x)+tan(3x+2)+cos^2(x)=5 which I just made it) it may not be possible to find an explicit solution. What does that mean...

$\tiny{t1.11}$ $\textsf{Evaluate the Integral}$ \begin{align*}\displaystyle I_{11}&=\int \frac{\sin\sqrt{t}}{\sqrt{t\cos^3\sqrt{t}}}\, dt\\ &=\int\frac{\sin\sqrt{t}}{\sqrt{t}\cos^{3/2}\sqrt{t}}\, dt\\ u&=\cos\sqrt{t}\\...

My mother's boyfriend's son who is in 6th grade asked me a question about the math they are learning. I thought it wouldn't be too bad but I cannot for the life of me figure it out. A solution would be greatly appreciated. 1. Homework Statement https://postimg.org/image/1tsa4v4t8r/ Homework...

Homework Statement Sino - ucos o =x Homework Equations N.A. The Attempt at a Solution I am asking if it's possible to make theta(o) the subject of formula in relation to some physics homework which I narrowed down to this but I don't know how to solve for theta, x is a known value but it's...