Newbetuts

Show that $1+\cos(\theta)+\cos(2\theta)+\cos(3\theta)+\cos(4\theta)+\cos(5\theta)+\cos(6\theta) = 0$

Another math contest problem: $\int_0^{\frac{\ln^22}4}\,\frac{\arccos\frac{\exp\sqrt x}{\sqrt2}}{1-\exp\sqrt{4\,x}}dx$

Prove $3(\sin x-\cos x)^4 + 6(\sin x+ \cos x)^2 + 4(\sin^6 x + \cos^6 x) -13 = 0$

Closed-form of $\int_0^{\pi/2}\frac{\sin^2x\arctan\left(\cos^2x\right)}{\sin^4x+\cos^4x}\,dx$

$\sin ^6x+\cos ^6x=\frac{1}{8}\left(3\cos 4x+5\right)$, Any quick methods?

Writing a Polar Equation for the Graph of an Implicit Cartesian Equation

Proof of $\arctan{2} = \pi/2 -\arctan{1/2}$

Computing arctan in the range $-\pi\leq \theta\leq\pi$

Why are there two versions of a polar equation for a circle from geometric form

Product of Sines and Sums of Squares of Tangents

How to evaluate the integral $\int_0^{\pi/2}x^2(\sin x+\cos x)^3\sqrt{\sin x\cos x} \, dx$?

$x_{0}= \cos \frac{2\pi }{21}+ \cos \frac{8\pi }{21}+ \cos\frac{10\pi }{21}$

Prove that a triangle with a given base and angle must be isosceles to have maximum perimeter

Show $f(x) = x^3 - \sin^2{x} \tan{x} < 0$ on $(0, \frac{\pi}{2})$

$\int_{-\pi/2}^{\pi/2} \frac{\sin^{2012}{x}}{\left(1+ \alpha^x\right)\left(\sin^{2012} {x}+\cos^{2012}{x}\right)}\;{dx} $

Find $ \sin \left( \theta _{1}\right) ^{2}+ \sin \left( \theta _{2}\right) ^{2}+ \sin \left( \theta _{3}\right) ^{2}=? $

Formula for ellipse formed from projecting a tilted circle onto the xy plane

Geometric interpretation of a quintic's roots as a pentagon?

New posts in trigonometry

Show that $1+\cos(\theta)+\cos(2\theta)+\cos(3\theta)+\cos(4\theta)+\cos(5\theta)+\cos(6\theta) = 0$

Is my trig result unique?

A matrix w/integer eigenvalues and trigonometric identity

Another math contest problem: $\int_0^{\frac{\ln^22}4}\,\frac{\arccos\frac{\exp\sqrt x}{\sqrt2}}{1-\exp\sqrt{4\,x}}dx$

Prove $3(\sin x-\cos x)^4 + 6(\sin x+ \cos x)^2 + 4(\sin^6 x + \cos^6 x) -13 = 0$

Closed-form of $\int_0^{\pi/2}\frac{\sin^2x\arctan\left(\cos^2x\right)}{\sin^4x+\cos^4x}\,dx$

$\sin ^6x+\cos ^6x=\frac{1}{8}\left(3\cos 4x+5\right)$, Any quick methods?

Writing a Polar Equation for the Graph of an Implicit Cartesian Equation

Proof of $\arctan{2} = \pi/2 -\arctan{1/2}$

Computing arctan in the range $-\pi\leq \theta\leq\pi$

Why are there two versions of a polar equation for a circle from geometric form

Product of Sines and Sums of Squares of Tangents

How to evaluate the integral $\int_0^{\pi/2}x^2(\sin x+\cos x)^3\sqrt{\sin x\cos x} \, dx$?

$x_{0}= \cos \frac{2\pi }{21}+ \cos \frac{8\pi }{21}+ \cos\frac{10\pi }{21}$

Prove that a triangle with a given base and angle must be isosceles to have maximum perimeter

Show $f(x) = x^3 - \sin^2{x} \tan{x} < 0$ on $(0, \frac{\pi}{2})$

$\int_{-\pi/2}^{\pi/2} \frac{\sin^{2012}{x}}{\left(1+ \alpha^x\right)\left(\sin^{2012} {x}+\cos^{2012}{x}\right)}\;{dx} $

Find $ \sin \left( \theta _{1}\right) ^{2}+ \sin \left( \theta _{2}\right) ^{2}+ \sin \left( \theta _{3}\right) ^{2}=? $

Formula for ellipse formed from projecting a tilted circle onto the xy plane

Geometric interpretation of a quintic's roots as a pentagon?