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A Golden Ratio Symphony! Why so many golden ratios in a relatively simple golden ratio construction with square and circle?

If $x\in \left(0,\frac{\pi}{4}\right)$ then $\frac{\cos x}{(\sin^2 x)(\cos x-\sin x)}>8$

Prove that $\measuredangle\gamma= 90^{\circ}$

Why $x^{n}=1$'s solution is equal to regular polygon in complex plane?

Evaluation of $ \sum_{k=0}^n \cos k\theta $

How to evaluate the limit $\lim_{x\to 0} \frac{1-\cos(4x)}{\sin^2(7x)}$

Find this $a,b,c$ such that $\sqrt{9-8\sin 50^{\circ}}=a+b\sin c^{\circ}$

Why is the graph of the implicit relation $\sin(x^2+y^2) = \cos(xy)$ so cool?

Integrate $I(a) = \int_0^{\pi/2} \frac{dx}{1-a\sin x}$

How do I parametrize a circle that's not centered at the origin?

How prove this equation has only one solution $\cos{(2x)}+\cos{x}\cdot\cos{(\sqrt{(\pi-3x)(\pi+x)}})=0$

Is the tangent function (like in trig) and tangent lines the same?

Unsure if I have solved/proven this trigonometric inequality.

Calculating $\lim_{x \to 0}\frac{x \tan2x-2x\tan x}{(1-\cos2x)^2}$

In Triangle, $\sin\frac A2\!+\!\sin\frac B2\!+\!\sin\frac C2\!-\!1\!=\!4\sin\frac{\pi -A}4\sin\frac{\pi -B}4\sin\frac{\pi-C}4$

What is the correct way to solve $\sin(2x)=\sin(x)$

My school mysterious trigonometry test question

New posts in trigonometry

Why does $\sin(45)=\frac{\sqrt2}{2}$ when $45^{\circ}= \frac{\pi}{4}$ radians?

Why is $\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha$

Sine inequality: How to prove that $|\sin(x)| \le |x|$ for $ x \in \mathbb{R}$ [closed]

A Golden Ratio Symphony! Why so many golden ratios in a relatively simple golden ratio construction with square and circle?

If $x\in \left(0,\frac{\pi}{4}\right)$ then $\frac{\cos x}{(\sin^2 x)(\cos x-\sin x)}>8$

Prove that $\measuredangle\gamma= 90^{\circ}$

Why $x^{n}=1$'s solution is equal to regular polygon in complex plane?

Evaluation of $ \sum_{k=0}^n \cos k\theta $

How to evaluate the limit $\lim_{x\to 0} \frac{1-\cos(4x)}{\sin^2(7x)}$

Find this $a,b,c$ such that $\sqrt{9-8\sin 50^{\circ}}=a+b\sin c^{\circ}$

Why is the graph of the implicit relation $\sin(x^2+y^2) = \cos(xy)$ so cool?

Integrate $I(a) = \int_0^{\pi/2} \frac{dx}{1-a\sin x}$

How do I parametrize a circle that's not centered at the origin?

How prove this equation has only one solution $\cos{(2x)}+\cos{x}\cdot\cos{(\sqrt{(\pi-3x)(\pi+x)}})=0$

Is the tangent function (like in trig) and tangent lines the same?

Unsure if I have solved/proven this trigonometric inequality.

Calculating $\lim_{x \to 0}\frac{x \tan2x-2x\tan x}{(1-\cos2x)^2}$

In Triangle, $\sin\frac A2\!+\!\sin\frac B2\!+\!\sin\frac C2\!-\!1\!=\!4\sin\frac{\pi -A}4\sin\frac{\pi -B}4\sin\frac{\pi-C}4$

What is the correct way to solve $\sin(2x)=\sin(x)$

My school mysterious trigonometry test question