Tan Definition and 152 Threads

Attempt : I could not progress far, but the following is what I could do. $$\begin{align*} \mathbf{\text{LHS}} & = (\tan A+\tan B+\tan C)(\cot A+\cot B+\cot C) \\ & = 3+\tan A \cot B+\tan B \cot A+\tan A \cot C+\tan C \cot A+\tan B \cot C+\tan C \cot B\\ & = 3+\frac{\tan^2A+\tan^2B}{\tan A \tan...

Hello, If I wanted to verify tan(x)cos(x) = sin(x), what about when x is pi/2? LHS has a restricted domain so it can't equal sin(x). Does this equation only work with a restricted domain? Nothing in my textbook discusses that. Thank you

I've been able to find the tangent line with most equations, but I don't have any idea how to do it with a range of values instead of being given a singular value.

One of my solutions had this in one part. Why is this the case?

import numpy as np import matplotlib.pyplot as plt x=np.arange(-5*np.pi, 5*np.pi, step = 0.02) plt.ylim(-1, 1) tan=np.tan(x) arctan=np.arctan(x) plt.plot(x,tan) plt.plot(x,arctan) Here is the code I came up with using the guide my teacher gave me, is this correct the way I have done it? Thank...

I calculated an expression for the derivative of the inverse tan but I did not use the identity as suggested. Why did I need to use this identity. Did I do the problem correctly? I got the correct answer. I tried to do the derivative of the inverse sin the same way. I used the same figure 1 on...

$\tiny{213(DOY)}$ $\displaystyle\int \sec x \tan x \: dx =$ (A) $\sec x + C$ (B) $\tan x + C$ (C) $\dfrac{\sec^2 x}{2}+ C$ (D) $\dfrac {tan^2 x}{2}+C $ (E) $\dfrac{\sec^2 x \tan^2 x }{2}+ C$

Prove that $$\tan18^\circ\ =\ \sqrt{1-\dfrac2{\sqrt5}}.$$ No calculator, computer program, Excel, Google, or any other kind of cheating tool allowed. (Smirk) Have fun!

Show that, $$\int_{0}^{\pi/2}{\ln^2 (\tan^2 \theta)\over \pi^2+\ln^2 (\tan^2 \theta)}\mathrm d\theta=\color{red}{\pi\over 2}\color{green}(1-\ln 2)$$

Hi! In one of my textbook i saw the relation tan(x) = x where x is very small value and expressed in radians. I want to know why its true and how it actually works. I would appreciate someone's help :smile:

given: 128kg F1 = 28 N, F2 = 57 N, F3 = 38 N, θ1 = 30°, and θ3 = 60°.They are asking for the angle (measured relative to the positive direction of the x axis in the range of (-180°, 180°]) of the asteroid's acceleration? The problem is displayed on quadrant I and IV for vector notation I got...

Homework Statement Homework Equations I didn't understand the first step. If tan (z) = a + ib, how can tan (z conjugate) be a - ib? tan is not a linear function. I know conjugates. x + iy, conjugate is x - iy But here the tan function is there. The Attempt at a Solution ...

Homework Statement there is one question limx--->0tanx-sinx/x3 i actually tried to seprate tanx and sinx amd then i multiplied and divided by tan2x and sin2x so that i can make tan3x/x3and sin3x/x3 to be 1 and in the end sin2x canceled and i got the answer as -1 which is wrong what errror...

I found in a book that the domain of tan x was {(2n+1)π/2 , n∈I} The graph however shows that for every value of x , the function takes on a value .So, why is the domain like this?

This is the continuation of the below thread: https://www.physicsforums.com/threads/what-is-integral-tan-2x-dx.856530/ Can someone please tell me how to integrate tan 2x dx?

From the Wikipedia article https://en.wikipedia.org/wiki/Small-angle_approximation, it says that they are "second-order approximations." What makes all three second order? Shouldn't sin and tan be first-order and cos be second-order?

I am eager to learn trigonometry. I have to be introduced to terms such as-sin,cos,tan,cosec etc. The internet"s explanation is going over my head. Can someone make them understand to me individually with the meaning of titha.(I cannot show its symbol , as it is not on the keyboard.) I will...

Homework Statement Hello! Surprisingly I get different results when I try to compute the inverse tangent function. My goal is to compute it both manually and using calculator in radiant mode. Homework Equations My goal is to compute arctan(½) both manually and using calculator in radiant...

I'm following this video: The professor says that for small angles, tan(Θ) = dy/dx. I don't understand why this is so. Tan(Θ) is equal to sin(Θ) / cos(Θ), and if Θ is small, then cos(Θ) is about 1, which means dx = 1, not a infinitesimally small number.

if y = tan inverse (cot x) + cot inverse (tan x)

find : (1)$ tan \,\, 15^o$ (2)$cos\,\,72^o$ (using geometry)

Homework Statement Under #3 Homework Equations Trig identities The Attempt at a Solution The picture attached is my attempt. The square in the upper upper left is the problem and the one in the lower right is my solution. I'm seeing that I'm getting the wrong answer, but not how.

This question occurred to me a few days ago and it's been bugging me ever since. Consider a circle in the coordinate plane with center P(x,y) and radius R, where R < D, D being the distance from the origin to the circle's center. There are two lines tangent to the circle (T1 and T2) that pass...

How can I write ## \tan ( \arcsin x) ## as ## \frac{x}{\sqrt{1-x^2}} ##? This is not a problem in itself but a part of a solution to a problem.

If sin \theta =\frac{4}{5} , find cos \theta and tan \theta Can you help me to solve. :) Many thanks :)

Homework Statement Find all numbers x ∈ [0, 2π] satisfying tan x = cos x. Your answers should be expressed in radians, rounded to 4 decimal places. Show all your working. [You will need to use a scientific calculator that has buttons such as sin−1 or arcsin so as to be able to find the angles...

Homework Statement I am trying to prove that the coefficient of static friction is equal to the tan of the angle of incline. (You can find the proof of this from ) I set the angle of incline as my independent variable and had an angle range from 10 to 37.5 degrees. After setting the slope to...

I was reading about the area of regular pentagon and it said that tan\frac{\pi}{5}=\sqrt{5-2\sqrt{5}}. Where did it come from? Does tan\frac{\pi}{n} always equal \sqrt{n-2\sqrt{n}}? If yes, what is the proof?

What is ##\int \tan 2x \ dx##? What I get is ##\int \tan 2x \ dx## ##= \int \frac{\sin 2x}{\cos 2x} dx## ##= \int \frac{2 \sin x \cos x}{1 - 2 \sin^2 x}dx## let u = sin x then ##\frac{du}{dx} = \cos x## or du = cos x dx So ##= \int \frac{2 \sin x \cos x}{1 - 2 \sin^2 x}dx## ##= \int...

Find the function with the given derivative whose graph passes through point P. $$r'\left(\theta\right) =6+\sec^2 \left({\theta}\right), P\left(\frac{\pi}{4},0\right)$$ 6+sec^2(x) The phase shift appears to be 1 but not sure how to get that How do add another equation to desmos?

So I'm supposed to find the exact values of the sine, cosine, and tangent of an angle by using a sum or difference formula ( i.e. sin(x+y)=sin(x)cos(y)+cos(x)sin(y) ), but this is the angle I was given: ${-13\pi}/{12}$. How do I use a sum or difference formula to get the sin, cos, and tan of that?

Homework Statement Hi! I'm trying to find the points of intersection of a sinusoidal function and a line. The line is y=x/7. The function is y=sinx. Can someone tell me how to determine the number of intersections and exact intersections. I would also like to know if the same method can be...

hello everyone! I want to know how to verify cos sin tan I always feel confused when i am doing the physics exercises. are we always use cos when it is x-axis and use sin when it is y-axis?? I feel so confused.

The problem Show that the left side is equal to right side ## tan (\frac{x}{2}) = \frac{1-cos(x)}{sin(x)} ## The attempt ##\tan(\frac{x}{2}) = \frac{ sin(\frac{x}{2}) }{ cos (\frac{x}{2}) } = \frac{ sin^2(\frac{x}{2}) }{ cos ^2 (\frac{x}{2}) } = \frac{\frac{1-cos(x)}{2}}{\frac{1+cos(x)}{2}} =...

The answer to Cot(arc tan x)

Hi all, My name is Arijit Biswas. I have resumed learning maths after a long time and I am stuck with a simple problem in trigonometry. I need to find a general solution to the equation: sec2 2x = 1– tan 2x. I have worked out something i.e. 1) Multiply by cos2 2x and that makes the equation...

The problem I want to solve ##tan(a)=-1## where a is in degrees. The attempt ## tan(a)= \frac{sin(a)}{cos(a)}=-1 \ \ cos(a) \neq 0 \\ \frac{sin(a)}{cos(a)}=-1 \\ sin(a)=-cos(a) \\ -sin(a)=cos(a) \\ sin(-a)=cos(a) ## I have no idea how to continue from here.

The problem A right triangle has an angle a and we know that ##cos \ a = \frac{1}{3}##. What is ## tan \ (90°-a) ## The attempt I know that the ration between the adjacent side and the hypothenuse is 1/3. I am not interested in the real lengths of the sides. I can therefore calculate the...

The problem I have the triangle ABC where ∠C is 90°. The side AC is ## \sqrt{3} \ cm ## and the side BC is 1 cm. What is ∠A (α)? The attempt $$tan(a) = \frac{1}{\sqrt{3}}$$ The problem is that I have to calculate the exact value of α without any calculator. I tried to calculate the third...

Let $A,\,B$ be acute angles such that $\tan B=2015\sin A \cos A-2015\sin^2 A \tan B$. Find the greatest possible value of $\tan B$.

Hey Guys. I'm having a bit of a problem with my solving triangles book. I'm finding the book really easy but there's this one thing that I keep getting wrong. Whenever I'm working with degrees with decimal points my answer aways fluctuates slightly from the real answer. I must be doing something...

A particular problem with factoring has both of these, one in the denominator and one in the numerator, if it were algebra it would look like: x^2-1/x-1. The trouble is I've forgotten how to simplify this. I'm on taptalk.)

Homework Statement Hey guys. So basically I'm doing some Calc I homework and I'm working on the domain of this function: g(x) = √tan(2x+π) Homework Equations Now to determine the domain, I know that the function under the root cannot be negative. The Attempt at a Solution So after...

< Moderator Note -- Thread moved from the technical math forums (that's why the HH Template is not shown) > It's supposed to be a simple problem. But I can't for the life of me figure out how to go about it. I managed to find out cos θ using the cosine rule, but it is a very long expression and...

Homework Statement Suppose the function is y = a cot k(x−b) Then (give exact answers; you can type pi for π): a = b = k = Suppose the function is y = a tan k(x−b), where b > 0. Then: a = b = k = The Attempt at a Solution Then (give exact answers; you can type pi for π): a = 4...

Determine the values of sin v, cos v, and tan v at each point P(x, y) on the terminal arm of an angle v in standard position. (b) (3, 4) ( (d) (12, 5) (f) (7, 24) for b I was able to do tan \theta= y/x tan \theta= 4/3 \theta = 53.13 My textbook says I am wrong... doing an online...

hello! we know that in every right triangle there are the sin, cos, tan etc equations how do we prove that these equations are valid? eg. how do we prove that the adjacent of an angle divided by the hypotenuse of the triangle is always the same for that given angle? thanks

Homework Statement for this, my coefficient of x^4 which is 8/4! = 1/3 .. but the ans should be 13/24... can you tell me which part contain mistake? https://i.imgur.com/05NnrdM.jpg https://i.imgur.com/28Q9o51.jpg Homework Equations The Attempt at a Solution

Problem statement Solve each equation over the domain theta greater than or equal to 0, less than or equal to 2 pi: Sin theta= sin theta tan theta Revelant equations Problem statement I divided it by sin theta to get tan theta equal to 1. Tan theta=1 can occur in the first and third...

Just want to verify if I am correct in assuming that tan 6x is exactly the same thing as 6 tan x It's merely a matter of rearranging the variables of algebra's multiplicative identity, am I right?