Trigonometery Definition and 84 Threads

Hi! New to this forum and signed up because I've just started a foundation degree in mechanical engineering, and having been out of education for a very long time beforehand, getting back to grips with mathematics and the like! Anyway, I would like to ask for some advice on this problem, I know...

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...

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...

Homework Statement the point (log a, log b) exists on the unit circle. find the value of axb. round to the nearest thousandths. Homework Equations x2 + y2 = 1 The Attempt at a Solution x2+y2 = 1 loga2+logb2 =1 2loga+2logb = 1 2(loga+logb) = 1 loga + log b = 0.5 logb = 0.5−loga now i try...

This question occurred to me a few days ago and it's been bugging me ever since. Consider a circle in the coordinate plane with center P(x,y) and radius R, where R < D, D being the distance from the origin to the circle's center. There are two lines tangent to the circle (T1 and T2) that pass...

When I press these buttons on my calculator to find the third side or an angle in a triangle, what calculation is happening? What is the logic behind it all? I know it's a very basic question, but I am only in grade 10 and have not started Math yet this year.

Homework Statement A wheel of radius 42 mm is rolling without slipping and its centre O has a velocity 7.2 m/s in the direction shown. The slider B is driven by the link AB and A is connected to the wheel. If AC= 28.9 mm, AB= 73.9 mm and angle ACB= 73°, what is the velocity of the slider B...

Homework Statement The following equation is to be solved for all x: ## \cos(x) + \cos(3x) = \sin(x) + \sin(3x)## Homework Equations The tripple angle formulas: ## \cos(3x) = 4\cos^3(x) - 3\cos(x) ## ##\sin(3x) = 3\sin(x) - 4\sin^3(x) ## The Pythagorean trig identity: ## \sin^2(x) + \cos^2(x)...

The problem I am trying to write ##-sin 2x + \sqrt{3} \cos 2x ## as ## A \sin(2x+\phi)## without using this formula below ##a sin (x) + b cos (x) = c sin (x+v), \ \ c=\sqrt{a^2+b^2} \ ,\ \ \tan v = \frac{b}{a}## The attempt ##A \sin(2x+\phi) = A \cos(\phi) \sin(2x) + A \sin(\phi)...

Question: what is the smallest positive real number x with the property that the sine of x degrees is equal to the sine of x radian? My try: 0. But zero isn't a positive number. How do I even begin to solve it? I tried taking inverse on both sides of sin(theta)=sin(x), but that didn't help.

Question (and Answer): The answer is written in thin black, inc = increasing, dec = decreasing. Am I wrong anywhere? Thanks!

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...

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...

Homework Statement If 1/2<=x<=1 , then cos-1[ x/2 + (√(3-3x2))/2] + cos-1 x is equal to? Homework EquationsThe Attempt at a Solution Substituting x=cosθ = cos-1(cosθ) + cos-1 [ cos(θ)/2 + (√(3(1-cos2(θ)))/2] = θ + cos-1 [cos (π/3) cos θ + sin (π/3) sinθ] =...

the black triangle is given, and red triangle is me trying to work it out why is my trangle wrong? and what is the right triangle? someone is sliding down a slope, with 2ms-2 of acceleration (not actually given which direction, maybe I'm wrong there, but the person is acelerating at 2ms-2 down...

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 Question: Sum of all the solutions of the equation: ##tan^2 (33x) = cos(2x)-1## which lie in the interval ## [0, 314] ## is: (a) 5050 π (b) 4950 π (c) 5151 π (d) none of these The correct answer is: (b) 4950 π Homework Equations ## cos(2x) = 2cos^2(x) -1 ## The Attempt...

Homework Statement An athlete can cover 3.0 m for a standing long jump. Assuming that this athlete jumps at an angle of 45 degrees to the horizontal. calculate the speed at which the jumper can launch herself from a standing start. Assume g =10 ms^-2 and no air resistance Assume that horizontal...

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

I'am trying to prove \int e^{ix}cos(x) dx= \frac{1}{2}x-\frac{1}{4}ie^{2ix} Wolfram tells so http://integrals.wolfram.com/index.jsp?expr=e^%28i*x%29cos%28x%29&random=false But I am stuck in obtaining the first term: My step typically involved integration by parts: let u=e^{ix}cos(x) and...

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)...

-25FCosα + 1.5FSinα= -80 Can someone please solve this and tell what trigonometric identities are we going to be using this solving?

Ok, I have encountered this one a few hours ago: \int \frac{cos x}{\sqrt{a - b cos x}}dx I have tried all techniques I know, integration by part, half-angle formula, substitution, trigo approach, and so on, but it seems, I could not integrate this one. I am no noob in integration, but this one...

Im trying to solve for a constant in an equation and it involves taking the arctanh(6.55) and my calculator is giving me an error, is there a way around this?

Homework Statement A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball. If the first ball moves away with angle 30° to the original path, determine: a. the speed of the first ball after the collision. b. the speed and direction of the second ball after...

ƒ(ß)=.5sec(ß) + √[1+(sec2(ß)/4)+tan(ß)/√(2)] Without graphing it or using calculus find the minimum. I already know the answer but want to know how to do it. It s at π/12 and is something like 1.5. First off this is NOT a homework problem. I already know the answer is something like 1.5 at π/12...

Can I present the trigonometry functions (such as SinX, CosX, TanX, CotX) by using only- Log, Lan, multiplication, division, addition, subtraction, exponantion, nth root operations?

Homework Statement A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball. If the first ball moves away with angle 30° to the original path, determine: a. the speed of the first ball after the collision. b. the speed and direction of the second ball after...

As part of a personal musicology project I found myself with the mathematical model of a geometry which utilizes the equation a*(a/b)sin(pi*x) The only problem with this is that I need to take the integral from -1/2 <= x <= 1/2, and according to Wolfram Alpha no such integral exists. I can...

Hello, I'm looking to try to use a gyroscope to determine the rocking motion (just side to side - not back and forth) of a boat while it is traveling forward or sitting still in the water. Specifically, I'm looking for the boat's angle from vertical and this angle's velocity. Can I do this...

So I have been out of Math Courses for 5 years then this semester Spring Semester I completed Pre Algebra with an A, this Summer I have two Semesters of which I am taking College Algebra for Science and Engineering Majors and Plane Trigonometry. My question is during the Fall Semester should I...

The result of the integral of (1/2)sin2x dx with: upper limit x = arccos((R-h)/R) lower limit x = 0 is (-h^2+2Rh)/(2R^2) I can not seem to get this exact answer my workings yield: let u = 2x, du/dx = 2 therefore dx = du/2 Integral becomes (1/4) ∫ sinu du (with the same upper and lower...

I was asked to draw a free body diagram to derive the equation tan θ = µs for the following situation: A box sliding down an inclined plane. My FBD has 3 forces - gravitational forces pointing downward (horizontally) <-- longest vector - normal force perpendicular to the box - frictional...

Homework Statement Given sin x = (eix - e-ix) / 2i, I want to prove that arcsin x = -i ln(ix + √1 - x2) Homework Equations I know about the Euler's formula and complex number. But I have never learned about complex logarithms. The Attempt at a Solution I try to use x = sin y. But it seems...