# Tagged Questions

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

42 views

### Highschool Geometry: Finding Common Tangent

I can't seem to identify what the arrows are indicating in this question, obviously the two lines are parallel but what does it mean? I don't know where to begin. Any suggestions?
40 views

### Confused about integration over zeroes.

Does for example $\int_{-\pi}^{\pi} \sin(x) \, dx$ cancel out to zero (following WolframAlpha/normal integration technique), or do we have to take the absolute value of all the areas between bounds ...
40 views

79 views

117 views

### Establish the identity: tan u(csc u - sin u) = cos u

I'm struggling to establish the identity below: $$\tan\,u(\csc\,u - \sin\,u) = \cos\,u$$ I've ended up with: $${1 - 2\sin\,u \over \cos\,u}$$ I don't know if this is correct so far, and if it is, ...
127 views

### Evaluate the indicated trigonometric function

Question states: Assume that theta is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function $\tan \theta = 1/5;$ What is $\csc \theta$ ...
58 views

### Prove the following trigonometric identity

$$\frac{\tan{(\frac{\pi}{4}+x)}-\tan{(\frac{\pi}{4}-x)}}{\tan{(\frac{\pi}{4}+x)}+\tan{(\frac{\pi}{4}-x)}} = 2\sin{x}\cos{x}$$ ============== On L.H.S, I've tried to write it using the sum and ...
55 views

### Find the position of a circle tangent to two other circles

Say there are 3 circles, A, centered at point a, B centered at point b, and C, centered at point c. Each has a known radius independent of the others, Ar, Br, and Cr. The positions of a and b are ...
20 views

### Trigonometry / Sum of two angles (α + β) if sinα = 8/17 and sinβ = 15/17

Find the sum of two angles α and β if sinα = 8/17 and sinβ = 15/17 if they are A) acute B) obtuse How do you approuch this problem? I'm stuck at the begging. Please help.
23 views

### Rearrangement of harmonic oscillation formulae

Can anyone show me why the following identity is true? $$A\cos(\omega t) + B\sin(\omega t) = \sqrt{A^2+B^2}\cos\left(\omega t + \arctan\left({ \frac BA}\right)\right)$$ I ask this is relation to ...
25 views

### Inverse Trigonometry Plots ArcT(T(x))-Clarification

enter image description here The graphs are plots of functional forms $T^{-1}(T(x))$ where T is a trigonometric function:sine,cosine,tangent,cosecant,cotangent,and secant Can someone please explain ...
66 views

125 views

### Derivative of inverse cosecant?

I am slightly confused by this, because when I worked out the derivative of arccosec(x), my answer was $\frac{-1}{x\sqrt{x^2-1}}$, which agrees with the answers online. However this would imply that ...
84 views

### Simplifying inverse trigonometric functions

Given below is the question $$\sin^{-1}\sqrt{\frac{x}{1+x}}$$ I tried to put x as tany, siny, cosy nothing seems to be working. Looking forward to some quick help , I have an exam tomorrow :/
49 views

### Solutions $3 p\sin x - (p+\sin x)(p^2-p \sin x +\ sin ^{2} x) =1$

$3 p \sin x - (p+\sin x)(p^2-p \sin x + \sin ^{2} x) =1$ has a solution for $x$. Then number of integral solutions of $p$ are ?
39 views

67 views

### Solving trigonometrics functions/equations

My niece ask me to help her with a school assignment, but I can't identify what type of equation are we solving. For example: $\DeclareMathOperator{\tg}{tg}$ $$\sin\alpha=\frac{8\sqrt{11}}{9}$$ or: ...
908 views

### Why are logarithms of trigonometric functions useful?

I have noticed that in many trigonometric tables the logarithm of the trigonometric values are given. Why this is given and not the actual values of the trigonometric functions? For example, instead ...
53 views

### Simple physics simulation problem

for a engineering project i'm doing it would be easier to simulate certain things beforehand, to do that I need to do some rag doll physics. I have a leg consisting of two parts, the upper and lower ...
3k views

### Is there a relationship between trigonometric functions and their “co” functions?

We all know that sine is one over cosecant, cosine is one over secant, etc. But is there any relationship between sine and cosine, secant and cosecant, and tangent and cotangent? What I am asking ...
14 views

### pinpoint the position of devices

My question is I know the distances d1, d2 and d3, thats the only information I have access to, but am build a android app where I need to indicate the positions of where the devices that are ...