Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.

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3answers
111 views

Inequality for $\cot$

How can I prove that for all $t\in[0,\frac{\pi}{2}], \cot^2t\leq\frac{1}{t^2}\leq1+\cot^2t$, with $\cot$ the cotangent function ? Thank you
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1answer
123 views

The graph of $\cot$ is the image of the graph of $\tan$ by a simple transformation

How can I justify that the graph of the function cotangent : $\cot$ is the image of the graph of the function $\tan$ by a simple transformation.
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1answer
196 views

Solution for following trigonometric equation?

I have the following trigonometric equation in $\theta$: $$0=G_{\omega}(1/r^2)({\csc^2}\theta){(r\cos\theta-x)}^2+(\cot\theta)(r\cos\theta-x)+r\sin\theta-y.$$ Is there an analytical solution for ...
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votes
2answers
572 views

How do you simplify the addition of square root

$2\sqrt{x} + \sqrt{3}$ How do I simplify this?
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2answers
304 views

A complex number in the power of another complex number

I saw this question, and found a formula: $$=\cos \left( d\log |a+bi|+c\arctan \frac{d}{c}\right)+i\sin \left( d\log |a+bi|+c\arctan \frac{d}{c}\right).$$ Which I later translated to Microsoft Math ...
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votes
4answers
342 views

tan=sec? test questions

If $\theta$ is in quadrant 1 and $\tan(\theta) = .6$ then $\sec(\theta) = $? This seems pretty easy to me: $\tan^2(\theta)-\sec^2(\theta)=1$ $-\sec^2(\theta)=.64$ $\sec(\theta)=8$ Another one, ...
0
votes
2answers
183 views

solving $\sec (3 \beta + 10) = \csc (\beta + 8)$

$\sec (3 \beta + 10) = \csc (\beta + 8)$ (in degrees) I am supposed to find one solution, and the angles are acute. I do not know the answer or how to get the answer. It is confusing for me ...
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1answer
3k views

angle theta in standard position

I have no idea how to start this homework. Here is the question. Sketch a angle theta in standard position such that theta has the least possible positive measure, and the given point is on the ...
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2answers
506 views

How to solve trigonometric equation $\sin(x)+x\cdot \cos(x)=0$?

I'm facing the problem of solving $$\sin(x)+x \cdot \cos(x)=0$$ using $$\tan(x)=\sin(x)/\cos(x)$$ I end at $$x+\tan(x)=0$$ on the other hand, I also tried $\cos(x)= \pm ...
-1
votes
1answer
121 views

How to draw arrows by rotating lines in 3d space?

I am trying to figure out direction vectors of the arrowheads of an arrow. Basically I'm given a normalized direction vector ...
-1
votes
3answers
416 views

The limit of $\sin(1/x)$ as $x\to 0$ does not exists

Prove that the following limit does not exist. $$ \lim_{x\to 0} \sin\left(1 \over x\right) $$ Our definition of a limit: Let $L$ be a number and let ${\rm f}\left(x\right)$ be a function which is ...
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4answers
295 views

Geometry: Auxiliary Lines

Geometry: Auxiliary Lines Any idea about this problem? Would be very interesting to see a geometric solution.
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votes
1answer
526 views

Where is zero degrees on a graph

I am using the following formula to calculate the position of a point after rotation in my web application. x' = xcos(0) - ysin(0) y' = xsin(0) + ycos(0) But ...
-1
votes
1answer
194 views

I am so confused!

Alright, so I have a triangle that is part of a mesh (3d model) and I need to get the rotation of it's x,y and z axis. Did I say all that right? rotation of y axis ...
-2
votes
3answers
392 views

Limit of infinite loops of sin x as n tends to infinity [duplicate]

Show that $$lim_{n\to\infty} \text {sin sin ... sin x} = 0 $$ for all x. Note that the n here refers to the number of sin in the expression above.
-2
votes
1answer
69 views

Is the series convergent? If convergent what will be the limit? [closed]

Is the series $$\sum\tan^{-1} \left(\frac1{2k^2}\right)$$ convergent? If convergent what will be the limit?
-2
votes
3answers
317 views

Simplification of Sines and Cosines raised to a power - Fourier Series

I need urgent help simplifying a few sines and cosines into expressions involved sine and cosine to a maximum power of 1. e.g. $\sin^2x = 1/2 + 1/2\cos(2x)$ - this one is easy. $\sin^3x = \sin^2x ...
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votes
3answers
2k views

Finding the values of $\cos \frac{n\pi}{2}$ and $\sin \frac{n\pi}{2}$.

i know that the values of $\cos n\pi=(-1)^{n}$ and $\sin n\pi=0$. Now i want to know that what is the general expressions of $\cos \frac{n\pi}{2}$ and $\sin \frac{n\pi}{2}$.
-4
votes
1answer
224 views

Finding two sides of a triangle [duplicate]

Possible Duplicate: calculate sides of the right triangle if I know 1 side and all the angles I'm not sure how to do this with only 1 side given, but I have a right triangle with a 30 ...