Trigonometric equation Definition and 133 Threads

Multiplying the first equation by ##\sin\theta## throughout and the second by ##\cos\theta## throughout, we get ##1-\sin^2\theta=m\sin\theta\quad,\quad 1-\cos^2\theta=n\cos\theta##. Solving the two equations, ##\quad\sin\theta=\dfrac{-m+\sqrt{m^2+4}}{2}\quad,\quad...

Attempt : ##\begin{align}\tan(x+100^{\circ})&=\tan(x+50^{\circ})\tan x\tan(x-50^{\circ})\\ \Rightarrow \dfrac{\sin(x+100^{\circ})\cos x}{\cos(x+100^{\circ})\sin x}&=\dfrac{\sin(x+50^{\circ})\cos (x-50^{\circ})}{\cos(x+50^{\circ})\sin (x-50^{\circ})}\quad{\text{(Using tan x=sin x/cos x)}}\\...

Returning if I have to show the effort, I came to this: \frac{\sin4\alpha}{1+\cos4\alpha}\cdot\frac{\cos2\alpha}{1+\cos2\alpha}\cdot\frac{\cos\alpha}{1+\cos\alpha}=\tan\frac{\alpha}{2}. =...

I’m stuck on how to begin. I’ve tried to factor out sin theta from both of the terms on the left hand side but that led to nowhere. Could I have a hint on how to continue? Than you!

[FONT=times new roman]Problem Statement : [FONT=times new roman]Let me copy and paste the problem as it appears in the text : Attempt : I haven't been able to make any significant attempt at solving this problem, am afraid. I tried to reduce all the higher submultiple angles ##2\theta...

Solve the equation, $$cos ∅+ \sqrt 3⋅ sin ∅=1$$ in the interval, $$0≤∅≤2π$$

[FONT=times new roman]Problem Statement : [FONT=times new roman]Solve for ##x## : Attempt : If I take ##x=\tan\theta##, the L.H.S. reads $$\tan^{-1}\frac{1-\tan\theta}{1+\tan\theta}= \tan^{-1}\left[\tan\left(\frac{\pi}{4}-\theta \right) \right ]=\frac{\pi}{4}-\theta.$$ On going back to ##x##...

Can a situation at angle ##\theta## happen, where: ##d sin \theta = 3 \lambda## ##b sin \theta = 2 \lambda## ##d/b = 3/2##

Given : The equation ##\sin m\theta + \sin n\theta = 0##. Attempt : Using the formula for ##\text{sin C + sin D}## (see Relevant Equation 3 above), the given equation simplifies to \begin{equation*} 2 \sin \frac{(m+n)\theta}{2} \cos \frac{(m-n)\theta}{2} = 0 \end{equation*} This implies the...

cot^2θ+5cosecθ=4 cot^2θ+5cosecθ-4=0 cosec^2θ+5cosec-4-1=0 cosec^2θ+5cosec-5=0 Let u=cosecθ u^2+5u-5=0 Solve using the quadratic formula; u=(-5± 3√5)/2 u=(-5+ 3√5)/2=0.8541... Substitute cosecθ=u Therefore, cosecθ=0.8541 1/sinθ=0.8541 sinθ=1/0.8541=1.170... which is not true since sin x cannot be...

a. I have just plotted the graph using desmos and attached an image here. Clearly, there are two values of x that satisfy the equation in the range. Do I need to add anything to this statement, I feel the response is a little brief for the question? b. Using the trigonometric identities; tan...

I can’t get the angle, answer given is x=56.33 , x=9.545. (All steps before the equation are correct.)

Summary: https://www.physicsforums.com/threads/trigonometry-question.977263/ Here's the question. Find the solutions of the equation tan(x)=2cos(x)+1 if 0 ≤ x ≤ 2π. I know this question can be solved by observing the graph but is there any other ways (like algorithms OR some Trigonometry...

theta1 = 90- theta2 I substituted that into v^2*sin(2theta1)/g So I get v^2*sin(180-2theta2)/g Now I'm stuck. What do I do next?

Hi all, I am a self learner (graduated very long ago and rusty at math) working through the Riley, Hobson and Bence text, chapter 1. 1. Homework Statement Use the fact that ##sin(\pi/6) = 1/2## to prove that ##tan(π/12) = 2 − \sqrt{3}.## Homework Equations ##tan(2x) = \frac { 2 tan(x)} {1...

Homework Statement The equation; 0.966= -0.354sin(φ+60) + 0.935cos(φ+60) and we're trying to find φ. Homework Equations 3. The Attempt at a Solution [/B] (edited) I tried doing ^2; 0.933= 0.125sin2(φ+60) -2*0.331sin(φ+60)cos(φ+60) + 0.874cos2(φ+60) x=φ+60 0.933= 0.125sin2x - 0.331sin(2x) +...

I have a trigonometric equation 2\sin \left ( \frac{q\pi }{m} \right )-\sin \left ( \frac{q\pi }{2} \right )=0 and want to know what values m as a function of q could take to satisfy the equation. Both terms zero is the obvious solution: q=2n; m=2; n is an integer. But there are more solutions...

Homework Statement Homework Equations General Formula for Tan(a)=Tan(b) The Attempt at a Solution See the question I have uploaded. I have tried solving it this way, Firstly I applied the Quadratic Formula to get, Now we have two cases, CASE-1 When So General Formula here will...

Homework Statement The problem given is sin2(x) + tan2(x) = √2 2. Homework Equations The relevant equations would be any trigonometric identities The Attempt at a Solution sin2(x) + tan2(x) = √2 sin2(x) + (sin2(x)/cos2(x) ) = √2 [ cos2(x) sin2(x) + sin2(x) ]/ cos2(x) = √2 [ (1- sin2(x))...

Today,in our class, we received a trigonometric equation ##\sin^{10}{x}+\cos^{10}{x}=\frac{29}{16}\cos^4{2x}## Here is my attempt:

Homework Statement ##4y=cos\left(4πx+\frac{3}{2}\right)## Homework EquationsThe Attempt at a Solution In dividing both sides by 4, I got: ##y=\frac{1}{4}cos\left(πx+\frac{3}{8}\right)## But I am told this is incorrect. Not sure if dividing everything by 4 here is an allowable technique, or if...

Homework Statement ##\sin a + \cos b## = ##\frac{-1}{2}## ##\cos a + \sin b## = ##\frac{\sqrt 3}{2}## 0 < a < ##\pi/2## ##\pi/2## < b < ##\pi## a + b = ? By calculating sin (a+b) Homework EquationsThe Attempt at a Solution I tried : ##\sin a + \cos b = 2sin\frac{(a+b)}{2}cos\frac{(a-b)}{2}...

If 0 < x < 90, what is the solution of tan(2x - 5) = cot(x + 5)? I got stuck in tan(2x - 5)tan(x + 5) = 1. What should I do after that?

Homework Statement cos2x + cos x = 0 (0 <= x <= 360) Homework EquationsThe Attempt at a Solution cos2x + cos x = 0 2cos(3x)/2 cos(x)/2 = 0 3x/2 = 90 degrees x = 60 degrees x/2 = 90 x = 180 3x/2 = 270 x = 180 x/2 = 270 x = 540 (not qualified) is there any more possibility (answers) for x?

Could I please get help with the following question? f(x)=(2cos^2 x+3)^5/2 Any help would be very much appreciated:)

I've gotten to this point: v^2/2=gs(sin(α)+cos(α)*k) I'm suppost to get "k" from this equation can some help by showing me the steps because I'm a bit confused on how to do it.

Homework Statement Find the solution of the inequality ## \sqrt{5-2sin(x)}\geq6sin(x)-1 ## Answer: ## [\frac{\pi(12n-7)}{6} ,\frac{\pi(12n+1)}{6}]~~; n \in Z##Homework Equations None. The Attempt at a Solution There are two cases possible; Case-1: ##6sin(x)-1\geq0## or...

1. Find α(β) given that the sum of the 2 sides= ##(x+y)## and its third, ##z## is a constant for 0<β<180. You can imagine that there's two pieces of string connected between two points. One string is as long as the distance between the two points while the other string is longer. If you...

Good day :)! Please advise how to start with the following trigonometric equation: 6*Sin^2(x) - 3*Sin^2(2x) + Cos^2(x) = 0 To be honest, I do not know what is the first steps to start with. I have tried to start with: 5*Sin^2(x) + Sin^2(x) + Cos^2(x) - 3*Sin^2(2x) = 0 1 + 5*Sin^2(x) -...

Homework Statement :[/B] Solve for ##x ##: $$ \sin ^{-1} {x} +\sin ^{-1} {(1-x)} =\cos ^{-1} {x} $$ Answer given: ##0## or ##\frac {1}{2}##. Homework Equations :[/B] All relevant formulae on inverse circular functions may be used. The Attempt at a Solution :[/B] Please see the pic below...

Homework Statement :[/B] Find the general solution of the Trigonometric equation: $$3\sin ^2 {\theta} + 7\cos ^2 {\theta} =6$$ Given andwer: ##n\pi \pm \frac {\pi}{6}## Homework Equations :[/B] These equations may help: The Attempt at a Solution :[/B] Please see the pic below: It...

Homework Statement :[/B] Find the general solution of the equation: $$\tan {x}+\tan {2x}+\tan {3x}=0$$ Answer given: ##x=## ##\frac {n\pi}{3}##, ##n\pi \pm \alpha## where ##\tan {\alpha} = \frac {1}{\sqrt {2}}##. Homework Equations :[/B] These equations may be used: The Attempt at a...

Homework Statement :[/B] Find the general solution of the Trigonometric equation $$\sin {3x}+\sin {x}=\cos {6x}+\cos {4x} $$ Answers given are: ##(2n+1)\frac {\pi}{2}##, ##(4n+1)\frac {\pi}{14}## and ##(4n-1)\frac {\pi}{6}##. Homework Equations :[/B] Equations that may be used: The...

The number of real roots of the equation $$2cos \left( \frac {x^2 + x} {6} \right)=2^x + 2^{-x}$$ Answer options are : 0,1,2,∞ My approach : range of cos function is [-1,1] thus the RHS of the equation belongs to [-2,2] So, we have -2 ≤ 2x + 2-x ≤ 2 solving the right inequality, i got 2x...

Homework Statement Solve acos²θ+bsinθ+c=0 for all values 0≤θ≤360° a=16 b=6 c=-12 So 16cos²θ+6sinθ-12=0 Homework Equations Cos²x=1-Sin²x The Attempt at a Solution Identity: Cos²x=1-Sin²x 16(1-Sin²θ)+6Sinθ-12=0 16-16Sin²θ+6Sinθ-12=0 6Sinθ-16Sin²θ=12-16=-4 Divide by 2(?) 3Sinθ-8Sin²θ=-2...

Homework Statement Find all solutions of the equation in the interval [0, 2\pi]. sin6x+sin2x=0 Homework Equations Double Angle Formulas sin2x=2sinxcosx cos2x=cos^{2}x-sin^{2}x =2cos^{2}x-1 =1-2sin^{2}x (3 formulas for cos2x) tan2x=\dfrac{2tanx}{1-tan^{2}x} Sum to Product Formula...

Hi, I've tried to solve this equation: $(2-\sqrt{2})(1+\cos x)+\tan x=0$ and I've tried everything but nothing works...Does anybody have an idea?

Homework Statement \sin (x) = \frac{2}{3} and \sec (y) = \frac{5}{4}, where x and y lie between 0 and \frac{\pi}{2} evaluate \sin (x + y) Homework Equations Looked over some trig laws, don't think I saw anything that's too relevant. There \sec (x) = \frac{1}{\sin (x)} The Attempt at a...

Homework Statement The following equation is to be solved for all x: ## \cos(x) + \cos(3x) = \sin(x) + \sin(3x)## Homework Equations The tripple angle formulas: ## \cos(3x) = 4\cos^3(x) - 3\cos(x) ## ##\sin(3x) = 3\sin(x) - 4\sin^3(x) ## The Pythagorean trig identity: ## \sin^2(x) + \cos^2(x)...

i need help with question 4a. Thank to anyone who helped.

A=3sinx+4cosx and B=3cosx-4sinx if B = 4 find A. What i tried is to use 4=3cosx-4sinx and solve for cosx now cosx = (4+4sinx)/3 plug this into A I end up getting A = (25sinx+16)/3 am I correct?

Homework Statement is the circled part wrong ? Homework EquationsThe Attempt at a Solution how could 0.5 sin2theta = ( 1 + cos2theta ) / 2 ?

Homework Statement a) Differentiate the following equation with respect to: 1) θ 2) Φ 3) ψ (Ua - Ub)' * C * r where: C is a 3 x 3 rotation matrix: [ cos θ cos ψ, -cos Φ sin ψ + sin Φ sin θ cos ψ, sin Φ sin ψ + cos Φ sin θ cos ψ] [ cos θ sin ψ, cos Φ cos ψ + sin Φ sin θ sin...

Homework Statement ##tanx=\frac{(1+tan1)(1+tan2)-2}{(1-tan1)(1-tan2)-2}## find x Homework Equations 3. The Attempt at a Solution [/B] I tried multiplying through the paranthesis and arrived at ##tanx=\frac{(tan1tan2-1)+(tan2+tan1)}{(tan1tan2-1)-(tan2+tan1)}## and i don't know if this is any...

Homework Statement Question: Sum of all the solutions of the equation: ##tan^2 (33x) = cos(2x)-1## which lie in the interval ## [0, 314] ## is: (a) 5050 π (b) 4950 π (c) 5151 π (d) none of these The correct answer is: (b) 4950 π Homework Equations ## cos(2x) = 2cos^2(x) -1 ## The Attempt...

Homework Statement sin x = C*sin y Find y as a function of x for a given C>0. Homework Equations sin x = C*sin y The Attempt at a Solution This is not actually a problem from a book, but a problem I myself thought about. I was studying elastic collisions in SCM and I obtained 2 equations...

http://www5a.wolframalpha.com/Calculate/MSP/MSP238521i5b83i951f19c3000010ca05be63f0bfc0?MSPStoreType=image/gif&s=10&w=219.&h=85. How do I solve this? I know the answers, as Wolphram Alpha has given me only the answers without any steps to how they derived those answers. I know that sin(x)=√3/2...

Solve for $x$ such that $2\sin(x+30^\circ)\sin 16^\circ \sin 76^\circ=\sin 2028^\circ \sin 210^\circ$ for $0\lt x \lt 180^\circ$.

Solve sin2x= sqrt(2)/2 (using algebra) the interval is between 0 and 2pi i got the first two answers: pi/8 and 3pi/8, but i don t understand how to get the other two: 9pi/8 and 11pi/8. thanks!

Homework Statement In 2001, Windsor, Ontario received its maximum amount of sunlight, 15.28 hrs, on June 21, and its least amount of sunlight, 9.08 hrs, on December 21 Due to the Earth's revolution about the sun, the hours of daylight function is periodic. Determine an equation that can...