# Tagged Questions

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### Range of inverse trigonometric function

Find the range of $y$. $$y=\tan^{-1}\left(\frac{2x}{1+x^2}\right)$$ I used the following approach: Let $$x=\tan\theta$$ $$\therefore \theta=\tan^{-1}x$$ Since the principal solution of $\tan^{-1}$ ...
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### trigonometric function and identities [closed]

If sin(x) = 1/3 and sec(y) = 17/15, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (Enter an exact answer.) sin(x − y) I have absolute no idea what this ...
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### For a boat to float in a tidal wave the water must be 2.5 meters deep… (trig questions)

$$y=5+4.6\sin\left(\frac{t}{2}\right)$$ What is the period in hours? Simply $p=2\frac{\pi}{n}=4\pi$ which is $\pi$ per hour If the boat leaves the bay at midday what is the latest time it can return ...
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### What is the order of operations in trig functions?

Is $\sin(x)^2$ the same as $\sin^2(x)$ or $\sin(x^2)$? I thought it would mean the former interpretation, $\sin^2(x)$, rather than the latter, but my teacher and I had a long argument on this and in ...
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### How many points to span a goniometric wave and how to construct the goniometric function

I have two questions concerning the spanning of a simple trigonometric function: What is the minimum number of points to define/span a "simple" trigonometric wave in two dimensions? Is it possible ...
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### How to determine a general arithmetic sequence formula for two intersecting trig function

I have equations out of two trigonometric functions. For example $\cos(4\alpha$) = -$\sin(5\alpha)$ $\tan(0.5\alpha$) = 2 $\sin(\alpha)$ How can I determine a general arithmetic sequence formula ...
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### Range of a trigonometric function

Question: Prove that: $$0 \leq \frac{1 + \cos\theta}{2 + \sin\theta}\leq \frac{4}{3}$$ I have absolutely no idea how to proceed in this question. Please help me!
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### How to solve $\tan x=x^2$ in radians?

How to solve $\tan x=x^2$ with $x \in [0, 2\pi]$? I try with trigonometry and many ways but the numerical solutions seems to be difficult.
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### $\tan(x), \cot(x)$ function properties

Does $\tan(x)$ and $\cot(x)$ has symmetry axis? (like e.g $\cos(x)$ at $\pi k$ for $k \in \mathbb{Z}$), I tried think in the direction that $\sin(x)/\cos(x) = \tan(x)$ and both of them have symmetry ...
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### Trigonometric functions over arbitrary angles

Trigonometric functions over obtuse or arbitrary angles doesn't make sense. We can only imagine for eg. sin(x) for angles < 90 degrees because it represents the ratio of the opposite and ...