# 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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### Prove: $\frac{r_a}{bc} + \frac{r_b}{ca} + \frac{r_c}{ab} = \frac{1}{r} - \frac{1}{2R}$, for circumradius R, inradius $r$, and exradii $r_x$ [on hold]

In $\triangle ABC$, prove: $$\frac{r_a}{bc} + \frac{r_b}{ca} + \frac{r_c}{ab} = \frac{1}{r} - \frac{1}{2R}$$ for circumradius $R$, inradius $r$, and exradii $r_a$, $r_b$, $r_c$ in the standard ...
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### $\cos2\theta +\cos\theta +k = 0$ - set of all values of $k$ for which there is a solution

The set of all values of $k$ (real), such that the equation $\cos2\theta +\cos\theta +k = 0$ admits a solution for $\theta$ is? MY ATTEMPT: I substituted $\cos2\theta$ with $2\cos^2\theta - 1$. On ...
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### Sine identity involving (3/p) for prime p greater than 3.

I am working through Ireland and Rosen's "Classical Introduction to Modern Number Theory" and am very stuck on this problem (#34 in Chp 5, 2nd edition): Note that $(a/b)$ is the Legendre symbol (or ...
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### “Show” that the direction cosines of a vector satisfies…

"Show" that the direction cosines of a vector satisfies $$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$$ I am stumped on these things: "SHOW" that the direction cosines corresponds to a given ...
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### Need help solving a trigonometric equation

I am preparing for finals and there is one exercise in my book that i don`t know how to solve. $$\frac{\sin a}{\sin \frac{a}{b}}=b$$ I just need to solve this for b. I tried wolfram alpha but it does ...
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### Converting $\cos\phi$ into $\frac{1−t^2}{1+t^2}$, given that $t = \tan\frac{\phi}{2}$

I have to figure out the working to convert $\cos\phi$ into $\dfrac{1−t^2}{1+t^2}$, given that $t = \tan\dfrac{\phi}{2}$. It would be amazing if someone could help I've been trying to do it for ...
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### Intuition around why domain of x of arcsine and arccosine is [-1;1] for “real result” & domain for arctangent is all real numbers

Context I'm working my way through basic trig (this question has a focus on inverse trig functions, specifically arcsine, arccosine and arctangent ), using Khan Academy, wikipedia and some of "trig ...
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### Height of lighthouse based on angle difference

I have a question in my maths book: A lookout in a lighthouse tower can see two ships approaching the coast. Their angles of depression are 25° and 30°. If the ships are 100 m apart, show that the ...
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### Vectors applied on the arm [on hold]

I just received a maths question saying the body and its joints are subject to significant forces under load. Your challenge is to redesign a part of the body, and using vectors, explain how it could ...