What we can derive from the trigonometric addition theorem
Question: Show that \(\frac{\sin(\alpha + \beta)\sin(\alpha – \beta)}{\sin\alpha – \sin\beta}=\sin\alpha + \sin\beta\). Answer: Use \(\sin(\alpha \pm \beta) = \sin\alpha\cos\beta \pm […]
Trigonometric functions with a parametric representation – How to solve the simultaneous equations
Question: Here is a set of simultaneous equations, $\sin x = \cos y = \sin (y-x)$. The ranges are \(0 […]
Can you relate \(\tan \theta \) to \(\sin 2\theta\) and \(\cos 2\theta\)?
Question: When \(\tan\theta = -2\), find \(\cos 2\theta\) and \(\sin 2\theta\). Answer: Maybe, you don’t believe that you can derive […]
You will be cool if you handle with tangent!!
Question: Find \((\tan 15^o + \sqrt{3})^2\) without a calculator. Answer: It is not easy to obtain \(\tan 15^o\) without a […]
The big wave, Tsunami!
Tsunami is greatly shaken by the earthquake. Thus, the wavelength would become several tens of kilometers to several hundreds of […]
Music, sounds and waves… It’s amazing!
We are actually surrounded by many types of waves. Musical instruments are familiar to us to appreciate the waves of […]
The photoelectric effect and the mysterious facts that physicists used to think of
The photoelectric effect is the phenomenon that electrons jump out when light is shined on the surface of a metal. […]
Actually, this world cannot be represented by mathematical expressions!
The law of motion discovered by Newton can explain every movement in terms of force, mass and acceleration in principle. […]
He happened to leave a petri dish open and discovered a big stuff!
Let’s introduce a coincident scientific discovery. Fleming, who was a medical doctor, searched for substances with effective bactericidal action on […]
Only this makes you understand calculus!
Speaking of calculus, most of math and science students learn it at high school, I guess, but how many people, […]