Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles and other topics relating to measuring triangles.
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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 trigonometry complex-numbers trigonometric-series z-transform- 55
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? sequences-and-series trigonometry geometric-series- 1
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\... trigonometry- 25
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 ... geometry trigonometry inner-products- 21
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 ... trigonometry- 21
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} =... trigonometry- 1,856
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, ... trigonometry systems-of-equations triangulation- 31
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! trigonometry trigonometric-series- 11
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 ... trigonometry- 1
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 = ... trigonometry- 903
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+\... trigonometry systems-of-equations- 1
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 ... trigonometry- 68
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^{... trigonometry inverse-function- 23
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 trigonometry- 1
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: trigonometry- 3
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