# 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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### Finding the function of a sine graph that has both translation and transformation

I can't quite find a problem similar enough to this yet, and I need some serious help. Here is a photo of the graph of the function I am trying to find out: Sorry, but I don't have enough ...
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### How to integrate $\int{\frac{1}{\cos(x)}}dx$ using the substitution $u=\tan\left(\frac{x}2\right)$?

So far, I've tried out to reformulate: $$\int{\frac{1}{\cos(x)}}dx$$ to: $$\int{\frac{\sin(x)}{\cos(x)\sin(x)}}dx$$ which is basically: $$\int{\frac{\tan(x)}{\sin(x)}}dx$$ But I'm not sure if this is ...
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### Find solution for a trigonometric equation set

How can I solve $$\begin{cases} \sin^2(y_1) = \frac{1}{2}\sin^2(\frac{y_1+y_2}{2})\\ \sin^2(y_2) = \frac{1}{2}(\sin^2(\frac{y_1+y_2}{2})+1) \end{cases}$$ where $$\space y_1,y_2 \in [0,\frac{\pi}{2}]$$...
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### Why is De Moivre's theorem not generalised for $(\sin x+i\cos x)$?

A representation of the form $(\sin x+i\cos x)^n$ can be reduced as follows $$( \sin x + i \cos x )^n$$ $$( \cos (90-x) + i \sin(90-x) )^n$$ $$( \cos (90n - nx) + i \sin(90n - nx) )$$ Now for all ...
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### Illumination of light on wall

A search light rotating from point $P$ is positioned $50$m from two walls that are opposite eachother. The walls is long enough to make the light almost invisible at each end. The illumination of the ...
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### Trigonometry-circumcircle and sides of triangle.

How to prove that $$4R\sin A\sin B\sin C=a \cos A+b \cos B+c\cos C$$ where R is the radius of the circumcircle and $a$,$b$ and $c$ the respective sides of the triangle. I wrote $R=a/2\sin A$ and ...
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### Using trig substitution, how do you solve an integral when the leading coefficient under the radical isn't 1?

I'm currently studying for my calculus exam, and i've run into a problem that has given me tons of issues. It's not one i've worked on before(or even seen before) so i'm worried if I see one on my ...
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### How to find the coordinates where the altitude of a triangle intersects the base in 3 dimensions?

Assuming I know three completely random coordinates in 3d space that correspond with vertices of a triangle, how can I then find the point at which the altitude intersects the base? I know how to ...