Questions tagged [trigonometry]
Questions about trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles and other topics relating to measuring triangles.
30,387 questions
61
votes
16
answers
3k
views
Can someone explain to me how a formula for the sine function is derived?
I'm 14 years old, and I'm taking a geometry course over the summer to get ahead in school. We've reached a unit on right triangles and trigonometry. I have knowledge of mathematics up to Algebra 1, ...
2
votes
1
answer
72
views
Infinite sums of nested radicals with closed-form expressions involving π [closed]
I found a quite striking formula that I would like to share, and I am interested in whether it has already been discovered. I fear so, as my methods aren't quite creative or original, but I would like ...
- 29
-1
votes
0
answers
28
views
Calculating Steering Caster Angle [closed]
I'm conducting some DIY wheel alignment on a vehicle and have struck some conflicting information online.
The measurement in question is 'caster'. If you imagine that the front wheels each pivot ...
-6
votes
0
answers
43
views
Trigonometry need help please I'm confused [closed]
Given that the radius of a circle $r=2$ units,draw an arch length $s$ equal to $r$ which forms the angle $t$. Remember that when $r=s$, the angle formed is one radiant. Label the drawing appropriately....
2
votes
0
answers
47
views
A General and Systematic Treatment of Langley’s Adventitious Angles Problem
Consider the above setup, where the white stuff denotes given lines/angles/points, and the purple stuff is an extra construction (the line $DF$ is drawn parallel to $AB$ hence the purple angle really ...
- 65.9k
1
vote
0
answers
47
views
Maximizing sum of absolute values of sines [duplicate]
For some real numbers $0 \le a_1 \le a_2\le a_3 \le ...\le a_n \le 2\pi$, such that $\sum_{i=1}^n a_i =2\pi$, I am looking to maximize the value of: $$A =\sum_{i=1}^n |\sin(a_i)|$$
This problem came ...
- 383
1
vote
1
answer
90
views
Finding the limit value for a given percentage of total area of half sine wave. Mathamatical function needed!
I am working on a project to control a motor by cutting the AC half sine wave. Therefore I need a mathematical function to find what angle to stop cutting half sine wave to represent a given ...
- 13
0
votes
2
answers
81
views
Geometry - Difference of corresponding angles from an interior point P is constant. [closed]
I came across a question from a math olympiad, involving triangle geometry which goes as:
In a triangle $ABC$, a point $P$ in the interior of $\Delta{ABC}$ is such that
$$\measuredangle BPC-\...
- 59
-1
votes
6
answers
117
views
What are the maximum and minimum values of $\sin(x) + \cos(x)$ in $[0,2\pi]$? [duplicate]
We consider a function $h(x) = \sin(x) + \cos(x)$ for $x \in [0, 2\pi]$ and we want to determine the minimum and maximum values of this function.
Here is what I tried:
I thought maybe i could use the ...
- 11
0
votes
0
answers
60
views
Do we understand what causes trigonometric functions behave like that or are they just observations? [closed]
I am in my first semester studying C.S, and I really want to build a fundamental understanding of Maths.
I watched some videos about the trigonometric functions as I am studying linear transformations ...
-3
votes
0
answers
25
views
If any trigonometric equation has roots a,b then does the quadratic equation formed by the trigonometric functions have the root f(a) and f(b)? [closed]
If a trigonometric equation
asec(x)+btan(x)=c has roots a,b then
The quadratic equation formed by this equation i.e.
tan^2(x) - (2ac/(a^2-b^2))tan x + (c^2-b^2)/(a^2-b^2)=0 has roots tab (a) , tan(b)
...
1
vote
2
answers
95
views
If $\alpha$ and $\beta$ are roots of a trigonometric equation, are $\tan\alpha$ and $\tan\beta$ are the roots of the equation as well? [duplicate]
So, the original question is this:
If $\alpha$ and $\beta$ satisfy the equation $a\tan\theta + b\sec\theta = c$, find $\tan(\alpha+\beta)$.
Now, this equation can be simplified to:
$$ (a^2-b^2)\tan^...
- 21
7
votes
3
answers
139
views
Showing $1+\frac{1+\tan^2x}{(\tan x-\tan y)(\tan z-\tan x)}+\frac{1+\tan^2y}{(\tan y-\tan x)(\tan z-\tan y)}=\frac{\cos x\cos y}{\sin(x-z)\sin(y-z)}$
Context: In a work of mine, I need to simplify the following quantity
$$Q(x,y,z):=1+\frac{1+\tan(x)^2}{(\tan(x)-\tan(y))(\tan(z)-\tan(x))} + \frac{1+\tan(y)^2}{(\tan(y)-\tan(x))(\tan(z)-\tan(y))}.$$
...
- 155
6
votes
1
answer
148
views
Random Needle intersecting two sides of Equilateral Triangle
I am teaching a college course in probabilistic and stochastic geometry. Recently, I introduced the class to Buffon's needle and variants such as the Buffon-Laplace grid problem. However, they have ...
- 563
2
votes
1
answer
111
views
$\int_{m}^{n} \sin(\pi x)(rx)^{2k-1} dx$ > $\int_{m}^{n} \sin(\pi x)(rx)^{2k+1} dx$
I am struggling with the following problem:
Suppose that $0 < m < n < \frac{1}{r}$, where $r$ is a small positive constant, $m$ is an even integer, and $n$ is an odd integer.
Let $I_k = \int_{...
