Trigonometry Definition and 664 Threads

Homework Statement If I have the following relation: tan(2x) = (B/2) / (A - C) but tan(2x) = sin(2x) / cos(2x) How do I obtain an expression for sin(x) and cos(x) in terms of the constants, B,A,C only? Homework Equations cos(2x) = 1- 2 sin^2(x) The Attempt at a Solution [/B] I can't...

Hi, If 2 people are holding a bag at an angle of 45 degrees each, and then only person is going to hold it, it is being said that the force that will have to be applied by that one person will be 1.5 times greater than when he was applying it together with the other. Can anyone explain this or...

Homework Statement Homework EquationsThe Attempt at a Solution 2sin3x=1 OR 2sin3x= -1 sin3x=1/2 sin3x= -1/2 From the unit circle and in accordance with the domain there are 3 solutions (B) But the answer is (C) HOW?

Hello. I am wondering how I can find the area of a trapezoid from its two legs and bases. My problem: ABCD is a trapezium with AB parallel to CD such that AB = 5, BC = 3, CD = 10 and AD = 4. What is the area of ABCD? If we trace a straight line from A down parallel to the height of the...

Homework Statement A pilot wishes to fly at maximum speed due north. The plane can fly at 100km/h in still air. A 30km/h wind blows from the south-east. Calculate: a) The direction the plane must head to fly north. b) Its speed relative to the ground. Homework Equations Sine Rule...

Here is a problem I found which is from a math class in 1957: A man is standing due East of a tower and notes it subtends an angles of 45 degrees with the tower. He walks South 42.4 feet and the subtended angle is 30 degrees. How tall is the tower? (You are only allowed to use only...

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...

Today,in our class, we received a trigonometric equation ##\sin^{10}{x}+\cos^{10}{x}=\frac{29}{16}\cos^4{2x}## Here is my attempt:

Homework Statement Show that ## {(tan φ+sec φ-1)/(tan φ-sec φ+1)}≡ {(1+sin φ)/cos φ}##[/B]Homework EquationsThe Attempt at a Solution ## (sin φ+1-cos φ)/(sin φ+cos φ-1)##[/B]

Hi, I'm making an electric longboard and trying to write an app for my phone to function as the remote. I've got a bunch of fancy Star-Trek-esque indicators on it, one of which is the pitch and roll of the deck. All the indicators have "danger zones" and turn red when they hit them, and for this...

Was just reading in Clifford A. Pickover's "The Math Book" that ants of the Sahara desert can, after wandering in a non-linear path to find food, from there go directly back home without a line of sight between the two locations. I don't see how one can arrive at the correct direction and...

(First, I am aware there is no cross product in higher dimensions. I am aware of differential forms. I am aware of the problems with the cross product. I know enough to know what I don't know. but set all that aside.) With that, could someone help me, by properly phrasing the cross product...

Homework Statement ##\sin a + \cos b## = ##\frac{-1}{2}## ##\cos a + \sin b## = ##\frac{\sqrt 3}{2}## 0 < a < ##\pi/2## ##\pi/2## < b < ##\pi## a + b = ? By calculating sin (a+b) Homework EquationsThe Attempt at a Solution I tried : ##\sin a + \cos b = 2sin\frac{(a+b)}{2}cos\frac{(a-b)}{2}...

Homework Statement Convert 24*8'15'' to Degree Decimal notation. Round to the nearest second. (Let * denote the 'degree' symbol. I couldn't find it anywhere in Latex) Homework EquationsThe Attempt at a Solution 24* + 8[(1)/(60)]* + 15[(1)/(3600)]* = 24.1375* This is the solution, before...

Homework Statement A subdivision lot is 200 ft long by 80 ft wide. A surveying crew made an error of 0.10 degrees when setting the iron pin in the corner of the lot shown. By what distance is the correct pin off of the true corner? Homework Equations I think I'm doing this one right...

Homework Statement A building is 400 ft tall and has suffered damage from a recent earthquake. If a surveyor is stationed 150 ft away, sets a zero angle on the bottom corner of the building, and turns the angle shown to the top of the building; what is the angle at which the building is leaning...

For one of my current projects in computer vision (which really is a study in point clustering and tracking in a data stream of n-dimensional data), I have come up with a way to very quickly index a 2D angle between two points or the angle of a vector. Doing a little bit of investigation, and...

What are some good books to learn spherical trigonometry from basics to the advanced level?

Mentor note: Moved thread to homework section ok So I'm doing supposedly easy trigonometry problems. i did the easiest ones. now I have no idea how to solve 2. first one is count sin+cos When tg - (1/tg) = -(7/12) what i figured is that i probably need to use...

Given that 0 < sin x < x is true for 0 < x < π/2. From the above, can we conclude that 0 < sin (x/2) < x/2? How about 0 < sin (x/5) < x/5? Why? How about 0<sin 3x < 3x ? Why?

Homework Statement A billiard ball moves at a speed of 4.00m/s and collides elastically with an identical stationary ball. As a result, the stationary ball flies away at a speed of 1.69m/s, as shown in Figure A2.12. Determine: the final speed and direction of the incoming ball after the...

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...

Can someone please tell me how sin(180 - x) = sin x? Here my attempt: sin (180 - x) = sin 180 . cos x - cos 180 . sin x Next? I have no idea...

Homework Statement I opened my old math book and interested in this Proof Cos (A-B) - tan(A-D) = (2cos A)/(sin 2A + sin 2B) Homework Equations Cos(A-B) = cosA cosB + sinA sinB Tan(A-D) = (Tan A - tan B)/(1+Tan A Tan B) The Attempt at a Solution cosA cosB + sinA sinB - (tan A - tan B)/(1+Tan...

Show that y≈∆φ×secφ in the jpeg attached. or ∆y = sec φ A and B are points on curved surface, two lines are extended through origin to a line that is tangent to the circle, these points are A' and B', change in Angle will bring a change in length between A' and B'. I need to know how is this...

!HELP! The Singapore Flyer, until recently the world's largest Ferris wheel, completes one rotation every 32 minutes.1 Measuring 150 m in diameter, the Flyer is set atop a terminal building, with a total height of 165 m from the ground to the top of the wheel. When viewed from Marina Centre, it...

1. By applying the sine rule we have $\displaystyle \begin{align*} \frac{\sin{ \left( A \right) }}{a} &= \frac{\sin{ \left( B \right) } }{b} \\ \frac{\sin{ \left( \alpha \right) }}{10} &= \frac{\sin{ \left( \beta \right) }}{8} \\ \frac{\frac{2}{3}}{10} &= \frac{\sin{ \left( \beta \right) }}{8}...

Once I complete high school geometry, I am planning to take algebra 2 and trigonometry next. I am asking if there are good textbooks out there that provide a full course of algebra 2 and trigonometry. Or should I take these two courses separately? By the way, I am self-studying.

Homework Statement Homework Equations cos 2theta = costheta^2 - sintheta^2 The Attempt at a Solution cos2theta = 1 2theta = 0, 2phi but i get wrong answer.. how is it?

I am making a video game using Game Maker Studio 2.0 and am making a radar. To give you some background, one object is obj_Player, and the other is obj_Sub. The radar gives the sub's position and distance from the player (center of radar). The first part of my radar works perfect. I normalized...

Homework Statement Hello! I am struggling with plotting polar graphs manually (without any help of the calculator). My main unresolved issue is with finding correct values of theta in a given range. For example, I have an equation: $r = cos(5\theta)$ Homework Equations and I know that the...

Homework Statement :[/B] Solve for ##x ##: $$ \sin ^{-1} {x} +\sin ^{-1} {(1-x)} =\cos ^{-1} {x} $$ Answer given: ##0## or ##\frac {1}{2}##. Homework Equations :[/B] All relevant formulae on inverse circular functions may be used. The Attempt at a Solution :[/B] Please see the pic below...

Homework Statement In any triangle ABC, prove that $$a^2 b^2 c^2 \left (\sin {2A} +\sin {2B} + \sin {2C} \right) = 32 \Delta ^3$$ Here ##\Delta ## means the area of the triangle.Homework Equations The Attempt at a Solution

Homework Statement In any triangle ABC, prove that $$ a^2 + b^2 +c^2 =4 \Delta (\cot {A}+\cot {B}+\cot {C}) $$ Homework Equations The Attempt at a Solution

In any triangle ABC, prove that $$(b+c-a) \left( \cot {\frac {B}{2}} + \cot {\frac {C}{2}} \right)=2a \cot {\frac {A}{2}} $$

I am facing a lot of problem in proving trigonometric results (advanced ones). There are a lot of formulas (compound angle related ones, transformation of sum into product ones and vice versa, multiple angle and sub-multiple angle ones). I am unable to figure out how to proceed forward in...

Homework Statement Calculate the following limit: Homework EquationsThe Attempt at a Solution I don't know how to proceed with this. I've tried to multiply by the conjugate, and to simplify the expression (x+\pi) to u, but I wasn't very sucessful. To what kind of algebric device I could...

Homework Statement [/B] In the equation between (3) and (2), why does the author says that ? Isn't the trigonometric identity actually ? 2. Homework Equations The Attempt at a Solution

I need help in solving this problem. Below shows all the measurements of the diagram, I need to find x:

Homework Statement Two spheres, with 0.5g each, are hanging by 30cm threads, tied on the same spot. The same electric charge is communicated to each sphere; in consequence, the threads move apart until they are about 60^\circ from each other. What is the value of the charge? \theta =...

Does these two picture cover everything about trigonometry ? Is anything important missing ?

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...

Homework Statement The machine tool diagram on the right shows a symmetric worm thread, in which a circular roller of diameter 1.5 inches sits. Find the amount d that the top of the roller rises above the top of the thread, given the information in the diagram. (Hint: Extend the slanted sides...

The average angle made by a curve ##f(x)## between ##x=a## and ##x=b## is: $$\alpha=\frac{\int_a^b\tan^{-1}{(f'(x))}}{b-a}$$ I don't think there should be any questions on that. Since ##f'(x)## is the value of ##\tan{\theta}## at every point, so ##tan^{-1}{(f'(x))}##, should be the angle made by...

I have been failing some tests on trig and one question was sinx=cos48. I have no clue what it means, please help

Hi, I've got this: $$\sin{(A*B)}\approx \frac{Si(B^2)-Si(A^2)}{2(\ln{B}-ln{A})}$$, whenever the RHS is defined and B is close to A ( I don't know how close). Here ##Si(x)## is the integral of ##\frac{\sin{x}}{x}## But, to check it, I need to evaluate the ##Si(x)## function. I'm new with Taylor...

A particle moves from point 0 to point 2. Both positions are known. The center of the circle and it's radius is also known. I am trying to work out the position of 1 where the particle strikes the circle. This is for a 2D astronomy simulator to work out where a particle will strike a 2D...

Homework Statement Suppose that a particle follows the path r(t) = 2cos(t)i + 2sin(t)j Give an equation (in the form of a formula involving x and y set equal to 0 ) whose whose solutions consist of the path of the particle. Homework Equations None that come to mind The Attempt at a Solution I...

Homework Statement [/B] Solve ##2sin3x.sinx=1##Homework EquationsThe Attempt at a Solution I used the identity ##( cos (A+B)= cos A cos B- sin A sin B), (cos(A-B) = cos A cos B+sinA sinB)→ -(cos 4x-cos2x)= 2sin 3xsinx, (cos 2x-cos4x=1)##now i am stuck , is this correct_ using ##(cos...

Why trigonometric functions are defined for unit circle, here "why" refers to what made them to define it this way, they may have defined it for right triangle only , can you give me a application where sin(120°) or sin, cos , tan of more than 90° is used to find some values like in physics or...