All questions with tag [math: trigonometry]


how was this angle found?

This is a remedy from a publication entailing trusses (in statics), I do not recognize just how they located the angle $\theta$. What is their method? This is the offered trouble: (the offered sizes vary a little bit in between the trouble in guide and also the remedy guidebook)
2022-07-25 17:47:21

Analytical method for root finding

Is there a logical method to locate the roots of the list below formula? $$y = -\frac{1}{2}{x}^{2}-\cos(x)+1.1$$ I'm sorry for the unimportant inquiry, I'm new at mathematics!
2022-07-25 17:46:40

Find the value of $A$, $n$ and $b$ if $y=A\sin(nt)+b$ has range $[2,8]$ and period $\frac{2\pi}{3}$.

A function with rule $y=A\sin(nt)+b$ has range $[2,8]$ and period $\frac{2\pi}{3}$. Find the value of $A$, $n$ and $b$. According to the teacher tip Do Dilations before translations But found translations first and I got $n$ , it is right? $\frac{2\pi}{3}n$=$2\pi$ $n=3$ But I don't know how to find $A$ and $b$. Many thanks.
2022-07-25 17:46:37

How to sketch $y=2\tan(x+\frac{\pi}{4})$ , $x \in (0,2\pi)$

How to sketch $y=2\tan(x+\frac{\pi}{4})$ , $x \in (0,2\pi)$ $2\tan$ , 2 is used to be amplitude in $\cos$ and $\sin$ graph but for the $\tan$ there is no amplitude,so where will that $2\tan$ sketch, also $x+\frac{\pi}{4}=\pi$ $x=\frac{4\pi}{4}-\frac{\pi}{4}$ $x=\frac{3\pi}{4}$ it is right? Can you please explain me in step by step and sho...
2022-07-25 17:45:30

Finding point coordinates of a perpendicular

Given that I recognize the factor works with of factor $A$ and also factor $B$ on sector $AB$ and also the anticipated size of a vertical sector $CA$ (vertical over $AB$), just how do I compute the factor works with of the factor $C$?
2022-07-25 17:43:26

Proving $\cos \theta = \sin\left(\frac{\pi}{2} - \theta\right)$ for all $\theta$

By drawing a right triangle it is obvious that $\cos \theta = \sin\left(\frac{\pi}{2} - \theta\right)$. I'm trying to prove to myself that this is true for all values of $\theta$ by following the reasoning on where the sine graph is inverted vertically by plugging in $-\theta$ and then shifted to the right by $\frac{\pi}{2}$ to get the cosine g...
2022-07-25 17:42:42

Complex roots of $z^3 + \bar{z} = 0$

I'm searching for the intricate roots of $z^3 + \bar{z} = 0$ making use of De Moivre. Some recommended increasing both sides by z first, yet that appears incorrect to me as it would certainly add a root (and also I would not recognize which root was the added ). I saw that $z=a+bi$ and also there exists $\theta$ such that the trigonometric dep...
2022-07-25 17:39:40

Understanding the Unit Circle

I'm mosting likely to require to recognize this (the device circle, English) for an examination, yet I'm so dreadful with both graphes and also memorization, the entire point is falling short to penetrate my mind. Making use of non - difficult English (essentially, I can be the dumbest individual below [at the very least I confessed, so be type...
2022-07-25 17:14:43

Show that $\forall n \in \mathbb{N} \left ( \left [(2+i)^n + (2-i)^n \right ]\in \mathbb{R} \right )$

Show that $\forall n \in \mathbb{N} \left ( \left [(2+i)^n + (2-i)^n \right ]\in \mathbb{R} \right )$ My Trig is actually corroded and also weak so I do not recognize the offered answer: $(2+i)^n + (2-i)^n $ $= \left ( \sqrt{5} \right )^n \left (\cos n\theta + i \sin n\theta \right ) + \left ( \sqrt{5} \right )^n \left (\cos (-n\theta) + i ...
2022-07-25 16:56:28

Finding $\tan t$ if $t=\sum_{i=1}^{\infty}\tan^{-1}\bigl(\frac{1}{2i^2}\bigr)$

I am solving this problem. Problem. If $$\sum_{i=1}^{\infty} \tan^{-1}\biggl(\frac{1}{2i^{2}}\biggr)= t$$ then find the value of $\tan{t}$. My solution is like the following: I can rewrite: \begin{align*} \tan^{-1}\biggl(\frac{1}{2i^{2}}\biggr) & = \tan^{-1}\biggl[\frac{(2i+1) - (2i-1)}{1+(2i+1)\cdot (2i-1)}\biggr] \\\ &= \tan^...
2022-07-25 16:55:53

When the trig functions moved from the right triangle to the unit circle?

I need to write a paper concerning the device circle and also I'm attempting to reveal several of its beginnings. Additionally, when the trig features were increased to angles more than $90^{\circ}$ and also what was the reasoning behind it? Additionally, why mirror the appropriate triangular along the axis as opposed to simply relocating the ...
2022-07-25 16:51:43

Goniometric simplification

Possible Duplicate: ¢ Proving that $ \frac{1}{\sin(45°)\sin(46°)}+\frac{1}{\sin(47°)\sin(48°)}+…+\frac{1}{\sin(133°)\sin(134°)}=\frac{1}{\sin(1°)}$ Simplify the adhering to amount $$ \frac{1}{\sin\left(1°\right)\sin\left(2°\right)} + \f...
2022-07-25 16:44:49

Working out two lengths when only one length and an angle is known on a right-angled triangle

I'm creating a first individual shooter video game, and also I've obtained until now. I'm currently attempting to create the code that fires a bullet. recognize what the carbon monoxide - ordinates of A are (this is where the personality is standing), and also I'm attempting to exercise what the carbon monoxide - ordinat...
2022-07-25 16:37:39

This second order Equation

Supposed that we have the formula ; $a\cos^2(x)+b\cos(x)+c=0$ in which $a,b,c$ are actual numbers. Clearly, the formula is created in regards to $\cos(x)$. My inquiry is if we could write it once more in regards to $\cos(2x)$ with the very same coefficients $a,b,c$ as over such that we have the very same remedies as the initial formula has? Many...
2022-07-25 13:31:16

How do I prove that $\sin(π/2+iy)=1/2(e^{y}+e^{−y})=\cosh y$?

How do I prove that $\sin(π/2+iy)=1/2(e^{y}+e^{−y})=\cosh y$? Can you help please?
2022-07-25 13:29:02

Average sine of an angle between two rays in a cone

I'm seeking an average value of sine of an angle in between 2 rays, existing within a cone with a particular angle. Offered a cone with an aperture of ${2\chi}$ and also 2 rays existing within the cone. The rays can be stood for as vectors in a round coordinate system: $$ {\vec{e_1}=\lbrace1,\phi_1,\theta_1 \rbrace},{\vec{e_2}=\lbrace1,\phi_2,...
2022-07-25 13:20:50

Calculate point, given x, y, angle, and distance

Excuse my lack of knowledge and also use wrong terms, yet I have x and also y works with, and also the angle that the entity is encountering on a 2D aircraft. I intend to locate the proper factor, claim 5 devices before the factor I have. Examples: If my entity is at 0, 0 and is facing east (0 degrees), my point would be 5, 0. If my entity i...
2022-07-25 13:13:55

Proof of identity $\ln \left|\frac{\sin x}{\cos x - 1}\right| = \ln \left|\frac{\cos x + 1}{\sin x}\right|$

How do you confirm this identification: $$\ln \left|\frac{\sin x}{\cos x - 1}\right| = \ln \left|\frac{\cos x + 1}{\sin x}\right|$$ Mathematica claims it holds true, yet if I attempt to streamline both sides, I end up with $$ \sin^2 x = \cos^2 x - 1$$ which ain't right.
2022-07-25 12:57:51

List the $x$-axis intercepts for this trigonometric function

Sketch the charts of each of the adhering to for $x$ in [0,2 $\pi$]. checklist the $x$ - axis intercepts of each chart for this period. $$y=\sqrt{2} \cos \left(x-\frac{\pi}{4}\right)+1$$ I attempted to address the formula $y = 0$ by executing the adhering to actions: $$\begin{align*} -1&=\sqrt{2} \cos\left(x-\frac{\pi}{4}\right) \\\\ ...
2022-07-25 12:51:21

Finding the distance between the centre of an arbitrarily rotated cylinder and a point on that cylinder

this is a little bit extra difficult than the blog post title recommends due to the fact that I was lacking words. I intend the complete title would certainly be: "Finding the range in between the centre of a randomly revolved cyndrical tube and also a factor on that particular cyndrical tube which is the junction of a ray predicted from th...
2022-07-25 12:49:49