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 […]
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 […]
Question: Here is a set of simultaneous equations, $\sin x = \cos y = \sin (y-x)$. The ranges are \(0 […]
Question: When \(\tan\theta = -2\), find \(\cos 2\theta\) and \(\sin 2\theta\). Answer: Maybe, you don’t believe that you can derive […]
Question: Find \((\tan 15^o + \sqrt{3})^2\) without a calculator. Answer: It is not easy to obtain \(\tan 15^o\) without a […]
Tsunami is greatly shaken by the earthquake. Thus, the wavelength would become several tens of kilometers to several hundreds of […]
We are actually surrounded by many types of waves. Musical instruments are familiar to us to appreciate the waves of […]
The photoelectric effect is the phenomenon that electrons jump out when light is shined on the surface of a metal. […]
The law of motion discovered by Newton can explain every movement in terms of force, mass and acceleration in principle. […]
Let’s introduce a coincident scientific discovery. Fleming, who was a medical doctor, searched for substances with effective bactericidal action on […]
Speaking of calculus, most of math and science students learn it at high school, I guess, but how many people, […]