Trigonometric Equations

How many distinct values of $x$ in the open interval $(0,\pi )$ satisfy the equation $\sin x + \sqrt...

The number of integer values of $k$ for which the equation $\cos x=\frac{k}{3}$ admits at least on...

The total number of solutions of the equation $2{\sin }^{2}x-3\sin x+1=0$ that lie within the inte...

Consider the general solution of $\tan 3x=\tan x$; the set of all real values of $x$ satisfying th...

The general solution of sin θ = 0 is

If $\cos \theta =\frac{3}{5}$ with $\theta$ in the first quadrant, then applying the half-angle iden...

By repeatedly using the triple-angle identity, the exact value of $\sin 3\theta$ when $\sin\theta = ...

Given that ${\tan }^{-1}x+{\tan }^{-1}y=\frac{\pi }{4}$ holds for positive reals with $xy<1$, the e...

The fundamental period of the composite function $g(x)={\sin }^{4}x+{\cos }^{4}x$, after simplification ...

In a triangle with sides $a$, $b$, $c$ and semiperimeter $s$, the area computed by Heron's formula f...

Applying the sine rule in a triangle where angle $A=30^{\circ }$, angle $B=45^{\circ }$, and the side ...

Statement based: assertion that ${\sin }^{-1}(\sin \frac{2\pi }{3})=\frac{2\pi }{3}$ and reason that arc...