I've tried to attempt the first part of the problem(spent over an hour on this) as second part could be easily optained with some calculus ,I asked my friend but alas nobody could conjure the solution to this dangerous trigonometric spell.
It was just pages and pages of concoction of...
My reasoning and answer is wrong, but I cannot figure out why.
Perhaps it is strange, perhaps not, but I want to figure out why my initial method of solving this problem did yield an incorrect answer.
I began by creating an equation and drawing a right triangle.
x is the horizontal part of...
Hi all,
I am a self learner (graduated very long ago and rusty at math) working through the Riley, Hobson and Bence text, chapter 1.
1. Homework Statement
Use the fact that ##sin(\pi/6) = 1/2## to prove that ##tan(π/12) = 2 − \sqrt{3}.##
2. Homework Equations
##tan(2x) = \frac { 2 tan(x)}...
I have the coordinates of a hurricane at a particular point defined on the surface of a sphere i.e. longitude and latitude. Now I want to transform these coordinates into a axisymmetric representation cylindrical coordinate i.e. radial and azimuth angle.
Is there a way to do the mathematical...
1. Homework Statement
A fish floats in water with its eye at the centre of an opaque walled full tank of water of circular cross section. When the fish look upwards, it can see a fish-eye view of the surrounding scene i.e. it is able to view the hemisphere of the scene above the water surface...
1. Homework Statement
A 70 kg window cleaner uses a 16 kg ladder that is 5.6 m long. He places one end on the ground 2.0 m from a wall, rests the upper end against a cracked window, and climbs the ladder. He is 3.5 m up along the ladder when the window breaks. Neglect friction between the...
For illustration purposes, I have attached an image of the line with the angle that I want to calculate. I am trying to determine the angle of rotation and the calculation that I am using currently is as below:
angle = math.atan2(y,x)
I use this formula to calculate the rotation for A and A'...
1. Homework Statement
2. Homework Equations
General Formula for Tan(a)=Tan(b)
3. The Attempt at a Solution
See the question I have uploaded.
I have tried solving it this way,
Firstly I applied the Quadratic Formula to get,
Now we have two cases,
CASE-1
When
So General Formula...
Hey guys, I would appreciate some help with the math behind creating a working coordinate system for a robotic arm. I am currently trying to determine what servo angles are necessary to align a robotic arm's claw to the given coordinates. Geometrically simplified, the robotic arm is a...
1. 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)
2. Homework Equations
3. The Attempt at a Solution
I tried :
##\sin a + \cos b =...
Hi! In one of my textbook i saw the relation tan(x) = x where x is very small value and expressed in radians. I want to know why its true and how it actually works. I would appreciate someone's help :smile:
1. Homework Statement
##\lim_{h \to 0} \frac{f(x - 2h) - f(x + h)}{g(x + 3h) - g(x-h)}##
While f(x) = cos x
g(x) = sin x
2. Homework Equations
3. The Attempt at a Solution
Using L Hopital i couldn't make it more simple.
I tried to divide it by cos and sin
Can you give me clue?
1. Homework Statement
A plane is taking off from an airport directly west of the airport it wishes to touch down in. The plane in still air can travel with a constant speed of 730 km/h. If a wind is blowing constantly at 92 km/h [45° S of E], at what angle must the plane fly to compensate for...
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...
I found in a book that the domain of tan x was {(2n+1)π/2 , n∈I}
The graph however shows that for every value of x , the function takes on a value .So, why is the domain like this?
1. Homework Statement
I am working on a report dealing with the velocity and acceleration of objects in Earth's surface based on distance from the Earth and thus far I have used the orbital speed equation and the acceleration equation. To get dive deeper into the math I would like to attempt...
1. Homework Statement
Find the solution of the inequality ## \sqrt{5-2sin(x)}\geq6sin(x)-1 ##
Answer: ## [\frac{\pi(12n-7)}{6} ,\frac{\pi(12n+1)}{6}]~~; n \in Z##
2. Homework Equations
None.
3. The Attempt at a Solution
There are two cases possible;
Case-1: ##6sin(x)-1\geq0##
or...
1. Find α(β) given that the sum of the 2 sides= ##(x+y)## and its third, ##z## is a constant for 0<β<180.
You can imagine that there's two pieces of string connected between two points. One string is as long as the distance between the two points while the other string is longer. If you...
1. Homework Statement :
Solve for ##x ##: $$ \sin ^{-1} {x} +\sin ^{-1} {(1-x)} =\cos ^{-1} {x} $$
Answer given: ##0## or ##\frac {1}{2}##.
2. Homework Equations :
All relevant formulae on inverse circular functions may be used.
3. The Attempt at a Solution :
Please see the pic below.
I...
1. Homework Statement :
Find the general solution of the Trigonometric equation: $$3\sin ^2 {\theta} + 7\cos ^2 {\theta} =6$$
Given andwer: ##n\pi \pm \frac {\pi}{6}##
2. Homework Equations :
These equations may help:
3. The Attempt at a Solution :
Please see the pic below:
It seems...
1. Homework Statement :
Find the general solution of the equation: $$\tan {x}+\tan {2x}+\tan {3x}=0$$
Answer given: ##x=## ##\frac {n\pi}{3}##, ##n\pi \pm \alpha## where ##\tan {\alpha} = \frac {1}{\sqrt {2}}##.
2. Homework Equations :
These equations may be used:
3. The Attempt at a...
1. Homework Statement :
Find the general solution of the Trigonometric equation $$\sin {3x}+\sin {x}=\cos {6x}+\cos {4x} $$
Answers given are: ##(2n+1)\frac {\pi}{2}##, ##(4n+1)\frac {\pi}{14}## and ##(4n-1)\frac {\pi}{6}##.
2. Homework Equations :
Equations that may be used:
3. The...
1. Homework Statement
Hello!
Last week I have came here for the help related to this problem. I am creating a new thread to describe the issue more precisely. I will be grateful for your help and explanation.
I post the explanation for the book first accompanied by attached pictures, and below...
1. 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.
2. Homework Equations
3. The Attempt at a Solution
1. Homework Statement
In any triangle ABC, prove that $$ a^2 + b^2 +c^2 =4 \Delta (\cot {A}+\cot {B}+\cot {C}) $$
2. Homework Equations
3. The Attempt at a Solution
1. Homework Statement
Hello!
Please, take a look at the exercise I post below. I have solved it correctly, and I understand how to solve it; so no problems here. But what I do have a problem with is the size of the angle between two points. Please, see details below. I will be grateful for your...
1. Homework Statement
Hello!
Please, help me to understand the task - I seem to fail to understand what goes where, and hence cannot proceed to solving the exercise. Please, take a look at the task, and then my questions. The task is on using the law of sines. Before trying to solve it I need...