Trigonometric Equations
Find the sum, in degrees, of all \(\theta\) between \(0^{\circ}\) and \(360^{\circ}\) such that
\[\tan(2\theta-330^{\circ})=\sqrt{3}.\]
by
Victor Loh
If \(\sec x + \tan x = \dfrac{22}{7}\) and \(\csc x + \cot x = \dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers, find \(m+n\).
by
Puneet Pinku
The smallest positive solution of the equation \[2 \sin^2 3x - \cos 8x - 1 = 0\] in the interval \(\left( 0, \frac{\pi}{2}\right)\) can be expressed in the form \(\frac{a\pi}{b}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).
by
Jaydee Lucero
The sum of all positive solutions of \[ 2\cos 2x \left( \cos 2x- \cos\frac { 2014 \pi ^ 2 }{ x } \right) =\cos { 4x } -1\] is \(k\pi \). Find \(k\).
by
shriya mandarapu
\[\large \cos(p \cdot \sin x)=\sin(p \cdot \cos x)\] Find the smallest positive integer \(p\) for which the above equation has a solution for \(x \in [0, 2\pi]\).
by
Sandeep Bhardwaj