# Tagged Questions

Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.

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### If $\cos\pi x=x^2-x-5/4$ then the value of $x$ is

If $\cos\pi x=x^2-x-5/4 \,$ then the value of $x$ is? I have completed: $\cos \pi x=(4x^2-4x-5)/4$ $\cos \pi x=3/8 \,$ or $1/8$
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### $x/|x|$ question about division

What is $\frac{x}{|x|}$ can it be simplified? Because look at this. $\frac{r\cosh(x)}{\sqrt{\cosh^2(x)}} = \frac{r\cosh(x)}{|\cosh(x)|}$ How do you do this?
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### How do you call this kind of functions in english?

I have a couple of formulas that I would like to plot, but I can't find the much needed documentation for them because I don't know how to correctly name them in english . This formulas assume that ...
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### How do we define the branch cuts for $\sin^{-1}z = \frac{1}{i} \log(\sqrt{1-z^2} + iz)$ as $(-\infty,-1)$ and $(1,\infty)$?

As $\sin^{-1}z$ is a function of complex $\log$, it is multivalued. The branch cuts to make $\log$ single-valued are defined conventionally as $-\pi < Arg(z) \leq \pi$. Why wouldn't this carry over ...
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### How to deduce the following trig relation?

How can I deduce: $$\sqrt{|x|}\sin(\frac{1}{x}) \le \sqrt{|x|}$$?? I know of the relation. $$\sin(u) \le u$$ $$u = \frac{1}{x}$$ $$\sin(1/x) \le \frac{1}{x}$$ But nothing related to $\sqrt{x}$ ...
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### Evaluation of $\int \frac{x\sin( \sqrt{ax^2+bx+c})}{ax^2+bx+c} \ dx\$

How do we find $$\int \frac{x\sin( \sqrt{ax^2+bx+c})}{ax^2+bx+c} \ dx\$$ NB: It is not mandatory that $ax^2+bx+c$ has only a single root
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### why tan θ > sin θ for range 0 to 90

(i) Prove the identity $$\tan^2 \theta - \sin^2 \theta \equiv \tan^2 \theta\sin^2\theta$$ (ii) Use this result to explain why $\tan θ > \sin θ$ for $0^\circ < \theta < 90^\circ$ I only need ...
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### Why $\sin(\pi)$ sometimes equal to $0$?

Simplify the statements. Which variables are free and which are bound? If the statement has no free variable, find out if the statement is true or false. Justify your answer. This was the ...
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### Evaluation of $\int \frac{x\sin(\sin x)}{x+5} \ dx$

How do we find $$\int \frac{x\sin(\sin x)}{x+5} \ dx\ ,$$ is there any way to take that $\sin x$ out from parent $\sin(\cdot)$ ?
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### Analytic Trigonometry

Find the exact values. $A)$ $\tan 60^\circ + \tan 225^\circ$ $B)$ $\tan 285^\circ$ (use $285^\circ = 60^\circ + 225^\circ$) I'm just confused on how to do these kind of problems when they are in ...
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### Which identity has been used here?

I have this written down in my notes, but I cannot remember how it came about: $$\sin(3t)\cos(10t) = 0.5(\sin (13t) + \sin (-7t))$$
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### Area of region in polar coordinates

I have to verify a point: I'm supposed to find the area of the region given in polar coordinates $$\sec{\theta}\le r\le 2\cos{\theta}$$ I plotted the curves of $\sec{\theta}$ and $2\cos{\theta}$ ...
### How do you get $\alpha$ from $\tan{\alpha}$?
How do you get $\alpha$ from $\tan{\alpha}$? Hello, I want to know how to obtain $\alpha$ from $\tan{\alpha}$. I mean, what is a formula (if there is one)? I know that it is schemes where it ...