# 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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### Tait-Bryan to Rotation matrix to translating from global to local space

Re-writing my entire question to be more math-oriented and hopefully make more sense. I have two objects, each at a position defined by P1 and P2 (XYZ). Each has a heading based on yaw/pitch/roll, ...
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### equation for the radius of a circle that is tangent to two lines and passing through a specific point on one of the lines?

I'm interested in finding the equation for the radius (and optionally the center point) for a circle that is tangent to two lines and passing through a specific point on one of the lines. So far, I've ...
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### Trying to find an $\arctan(x/y)$ identity.

I have this equation : $$\theta = \arctan\left(\tfrac xd\right) + \arctan\left(\tfrac yd\right).$$ $\theta$ is an angle and I am trying to express $d$ as a function of $\theta$. So is there a way ...
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### Implicit differentiation with trig function

I have the following expression which I need to implicitly differentiate: $$xy^2 + x^2 + y + \sin(x^2y) = 0$$ I'm a little confused as I'm not entirely sure what to do with the trig function. ...
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### Calculating the points of a annular sector type shape.

The problem involves a circle inside a square sharing a common center point. The circle is always smaller than the square so that their edges never intersect. Then an annular sector (see cyan shape in ...
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### Finding the vertical shift of a sinusoidal function

I'm currently studying sinusoids, I've been given a graph with a few key points and have been told to find a cosine function which fits it. When it comes to finding the vertical shift of the graph the ...
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### $m\cos^2{\theta} + n\sin^2{\theta} < l \implies \sqrt{m}\cos^2{\theta} + \sqrt{n}\sin^2{\theta} < \sqrt{l}$

Prove that $m\cos^2{\theta} + n\sin^2{\theta} < l \implies \sqrt{m}\cos^2{\theta} + \sqrt{n}\sin^2{\theta} < \sqrt{l}$ for every $m, n, l >0$.
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### Definite integral of trig function

I'm looking for some assistance on the following problem: Let $$T(x) = \int_{4r^3}^{4} tsin(t^3)dt$$ Find $$T'(r)$$ I'm struggling to find the antiderivative of the sine function, particularly as ...
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### Slight help with inverse trigonometry question

I apologize for the lack of LaTeX, i will try to learn LaTeX and update this question as soon as possible. I am having some trouble with an inverse trigonometry question and was hoping that someone ...
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### Evaluate an integral involving tangent and secant: $\int \tan^2x\sec^2x\,dx$

Evaluate $\displaystyle \int \tan^2x\sec^2x\,dx$ I tried several methods: First method was I changed $\tan^2x = \sec^2x-1$, and then substitute $\sec x$ to $t$, but it doesn't work. Second ...
I have an Equilateral triangle with unknown side $a$. The next thing I do is to make a random point inside the triangle P. The distance $|AP|=3 cm, |BP|=4 cm, |CP|=5 cm.$ What is the area of the ...