![Questions Tagged [Trigonometry]](https://docuprint.cloud68.co/uploads/questions-tagged-trigonometry_1200.jpg)
Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles and other topics relating to measuring triangles.
27,378
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Z transform of $\sin \alpha k$
Could anyone please explain how we got the second step (in terms of $e$ and $i$) after writing it in basic Z-transform notation? And how it was simplified? I can't follow
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1
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28
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Geometric sequences with trigonometry
For the following sum:
$\cos(2\theta) + \cos^2(2\theta) + \cos^3(2\theta) ...+ \cos^N(2\theta)$
Why is the range $\{0 < \theta <\frac{\pi}{2}\}$ for there to be a sum?
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Is there a way to use the Weierstrass Substitution for $n\theta$?
So, I was looking at the Wikipedia page for the tangent half-angle formula (or Weierstrass substitution) and I noticed something: Is there a similar set of substitutions as the ones below:
$$\cos\...
2
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1
answer
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Geometry - I am getting two different results when using two different scalar product properties
I am trying to solve a problem regarding the scalar product.
The problem has multiple choices, and I solved it in two different ways, and got different values. Both of the values were a choice, but ...
2
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3
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There exist real numbers $x$ and $y$ such that $\cos(x+y)=\cos x+\cos y$
I’m trying to either prove or disprove the statement that there exist real numbers x and y such that $\cos(x+y)=\cos x+\cos y$, though I quickly encountered a brick wall after expanding the LHS:
$\cos ...
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1
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Solve the equation $\overline{PC}^2 + 2 \overline{PD}^2 + 2\overline{AP}^2 = 7$ under some assumptions on those points.
Take $D$ and $C$ two points respectively on the tangents in $A$ and $B$ of a semicircle af diameter $AB$ with $\overline{AB} = 2$. Moreover chose $C$ and $D$ such that $\overline{AD} = \overline{CB} =...
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2
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How to solve the triangulation problem?
I have $3$ sensors. I've built the following system of equations that match the data from sensors. I need to find $x$, $y$, $R_a$, $R_b$, $R_c$, $\alpha$, $\beta$ and $\gamma$. Can you please help me, ...
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Help me solve these inverse trigonometry question, Question 25.17
Image link.
It is a series, I tried bringing it to a form through which it would reduce itself like a telescopic series but couldn't do much about it.
An abstract solution would do.
THANKS!
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Riemann's Sphere Scale Factor
If we considered Riemann's sphere as a stereographic projection to get a sphere onto a planar surface. I'm pretty sure these are this is the right formula from what I've seen, but I'd like to confirm ...
6
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2
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58
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Find the maximum perimeter of a right angled triangle with hypotenuse 1
This is a question from the grade 7 Math Competition. I can solve it by considering one of the angles, say $\theta$, besides the right angle. We have the perimeter given by $1+\cos\theta+\sin\theta = ...
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1
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Solving the system $x=a\cos\theta-b\sin(\frac\pi2-\beta+\theta)+c\cos\theta$, $y=a\sin\theta+b\cos(\frac\pi2-\beta+\theta)+c\sin\theta$
Its pretty simple, (a, b, c, x, & y), are known. I need to know theta and beta... Ive tried so many methods and I cant solve it...
$$x=a\cos\left(\theta\right)-b\sin\left(\frac{\pi}{2}-\beta+\...
2
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2
answers
93
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Solving $\tan(2x)\tan(x)=1$ two ways gives different solutions
While solving this Equation by 2 ways I am getting different solution
$$\tan(2x)\tan(x)=1$$
So, I solved it in two ways.
Method-1
This gives solution as:
x=nπ ± π/6
Which is also given as solution
...
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1
answer
52
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Graphing integer function $f(x) = [\sin^{-1}x]$
I have few difficulties when drawing inverse trigonometric functions graph. I am unable to draw the graph of $[\sin^{-1}x]$; the [$\cdot$] (the brackets] denote the greatest integer function of $\sin^{...
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How can I derive sin(A+B) from cos (A-B)? [closed]
The formula for cos (A-B)= cosAcosB+sinAsinB
From this the question wants me to derive sin(A+B). Please help
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2
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Solving $ \sqrt{ \frac{11 \cdot \sin(x)^2 - 2}{\sin(x)^2} + 5 \cdot \cot(x)} = 3 - \cot(x) $
I can't figure out how to solve these equations:
$$ \sqrt{ \frac{11 \cdot \sin(x)^2 - 2}{\sin(x)^2} + 5 \cdot \cot(x)} = 3 - \cot(x) $$
The answer should be like this:
