Tag: trigonometry
- Compute $\int_0^1\frac{\arctan(\lambda x)}{x\sqrt{1-x^2}}\mathrm dx$ and $\int_0^1\frac{\arctan(\lambda x)}{\sqrt{1-x^2}}\mathrm dx$
- Trigonometric equation $5 \sin(x) + 4\cos(x) – 10\sin(x)\cos(x) = 2$
- Range of $y=a\sin(x)+b\,\mathrm{cosec}(x)$ where $a$ and $b$ are real and $a,b\ne0$
- Optimization problem that involve square root in the constraint
- Can someone help me derive this formula for the hidden height of a distant object due to the curvature of the earth
- Which of the following values can the function $y = \tan(x)$ take on if $\frac{\pi}{2} \lt x \lt \frac{3\pi}{4}$ holds
- Showing ${\sin mx\over\sin x}=(-4)^{(m-1)/2}\prod_{j=1}^{(m-1)/2}\left(\sin^2x-\sin^2{2\pi j\over m}\right)$ for odd $m>0$ (from Serre’s “Arithmetic”)
- Solve this complicated trigonometric equation for the solution of this triangle.
- Prove or disprove that : $x^{\frac{\sin\left(x\right)}{x}}> \sin\left(x\right)+\frac{1}{x-1}$ for $x\geq \pi$
- Find the dihedral angle of shapes in higher dimensions