I am having trouble solving this word problem: A cellular tower that is 150ft is placed on top of a mountain that is 1200 feet above sea level. what is the angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 400 feet above […]

I am a little weak in trigonometry. I have two questions: Find the value of $\cos 52^{\circ} + \cos 68^{\circ} + \cos 172^{\circ} $ Find the value of $\sin 28^{\circ}+ \cos 17^{\circ} + \cos 28^{\circ} + \sin 17^{\circ} $ I am asking these questions because: 1. I am weak and unable to solve these. 2. […]

I’m a high school calculus/precalculus teacher, so forgive me if the question is a little basic. One of my (very gifted) students recently came up with a construction yielding a quartic, one of whose roots was sin(80º) — which led me to the startling discovery that this (and, indeed, all rational values of sine/cosine (in […]

According to my textbook: $$\int_{-L}^{L} \cos\frac{n \pi x}{L} \cos\frac{m \pi x}{L} dx = \begin{cases} 0 & \mbox{if } n \neq m \\ L & \mbox{if } n = m \neq 0 \\ 2L& \mbox{if } n = m = 0 \end{cases} $$ According to the trig identity given on this cheat sheet: $$ \cos{\alpha}\cos{\beta} = […]

Of course for $x\neq 0 $ and $\alpha$ in radians. Can you define them?

Prove that $\frac{\tan{x}}{\tan{y}}>\frac{x}{y} : \forall (0<y<x<\frac{\pi}{2})$. My try, considering $f(t)=\frac{\tan{x}}{\tan{y}}-\frac{x}{y}$ and derivating it to see whether the function is increasing in the given interval. I should be sure that $\lim_{x,y\rightarrow0}\frac{\tan{x}}{\tan{y}}-\frac{x}{y}\geq0$ for the previous derivative check to be useful, which I’m not yet, but I’m assuming it’s $0$ since I’d say that since both $x,y$ approach […]

What is value of $tanA$ if $2\tan(2A)+4\tan(4A)+\frac{8}{\tan(8A)}=0$ writing everything in $\tan(A)$ and solving for $t$ is next to impossible without maths engines. So i am seeking for a shorter way. Thanks

Let $L_n:$ the side length of a regular $n$-polygon inscribed in a unit fixed circle. We have an interesting relationship: $L_6^2+L_6^2=L_4^2$ $L_6^2+L_4^2=L_3^2$ $L_{10}^2+L_6^2=L_5^2$ There are more solutions: $L_m^2+L_n^2=L_p^2$ ?

High school students are learning about the basics of solving quadratics and trigonometric ratios, including trigonometric inverses. The eventual goal of their project is to be able to show a reasonable firing solution, given in initial angle $\theta$ and initial velocity $v_0$. Projectile motion is given by $$y=\left(\tan{\theta}\right)x-\left(\frac{g}{2v_0^2\cos^2{\theta}}\right)x^2$$ where $x$ and $y$ are horizontal and […]

How do you solve $\arctan(n)$ to radians by hand? I. e. $\arctan(1)$ >> process >> $\pi/4$ ::EDIT:: I have this taylor expansion that allows me to calculate an approximate value for arctan, but am wondering if there’s a closed-form solution (Or a more general formula than below):

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