# 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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### Trig funct graphs check (amplitude, period)

Hi for the following questions I was wondering if I was correct in my answers and if I am incorrect, please correct me. Thank You My solutions, please correct me if I am wrong. 2cosx, amplitude ...
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### Start and endpoint of line, creating arrow heads [closed]

I have a start point(5.6,4) and an endpoint (6.1,3.15) I want to make an arrow head at the start point that is an equilateral triangle(60 degrees) with a length of .1. How can I accomplish this? ...
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### Simplifying trig expression $\frac{1}{1-\cos \theta}$

I need help with the following trig problem, I'm getting the first part, but can't seem to complete it. $$\frac{\cos \theta}{1-\cos^2 \theta}- \frac{1}{1-\cos \theta}$$ The first part is going to ...
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### Find $\tan 2x$, given $\tan(x+y)=3$ and $\tan(x-y)=2$

I am having a hard time to solve this trigonometric system of equations. The equations is as follows: We are given $$\tan(x+y)=3$$ $$\tan(x-y) = 2$$ and we need to find $$\tan2x$$ I have ...
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### Bearings question confusion

At 12.00pm , a ship was spotted at a point P , 30 km due north of an island , L . The ship was sailing on a bearing of 120 degree at 32km/h . How far was the ship from the island at 12.30pm ? My ...
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### Why don't we take $\sin x$ as negative square root of $1-\cos^2x$? [closed]

I am confused of using $\sin x$ as as negative square root of $1-\cos^2x$. Can anyone help please?
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### Sides of a triangle are in Arithmetic Progression, then find $\tan (\alpha+ \frac{\beta}{2})$

The sides of a triangle are in Arithmetic Progression. If the smallest angle of the triangle is $\alpha$ and largest angle of the triangle exceeds the smallest angle by $\beta$, then find the value of ...
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### How to find $\tan \left(\frac{x}{2}\right)$ knowing that $\cos \left(x\right)+\sin \left(x\right)=\frac{7}{5}$

Good evening to everyone. I don't know how to find $\tan \left(\frac{x}{2}\right)$ knowing that $$\cos \left(x\right)+\sin \left(x\right)=\frac{7}{5}$$ and x$\in (0,\frac{\pi}{3})$ Here's what I've ...
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### Hypocycloid with an outer ellipse

I have tried to change the traditional hypocycloid a bit. What I've basically done is that a circle now rolls inside an ellipse. I am trying to find the equation for the same. I am mostly done, ...
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### Cycloids with ellipse

I have been researching about the epitrochoids and hypotrocoids lately. I was wondering if it would be possible for us to have an ellipse rolling around a circle? If so, then how could one derive its ...
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### A trigonometric problem when calculating distance to the boundary of a convex hull

Suppose we have a sphere and a point outside of the sphere. We denote the point outside as $v$ and the origin of the sphere as $x$. The convex hull of the sphere and $v$ should be like an ice cream ...