Trigonometry Definition and 662 Threads

Problem Statement : I copy and paste the statement of the problem directly from the text. Attempt : I wasn't able to go far into the solution. Below is a rough attempt. ##\begin{equation*} \begin{split} \sin^2A-\sin A\sin B+\sin^2B-\sin B\sin C+\sin^2C-\sin C\sin A & = 0\\ \sin A(\sin A -...

It is about that the rznge of 60 degrees = R of 30 degrees, but how would I prove that? Sin(120) needs to equal sin(60) How can i prove that theyll be the same range(without air resistance?) My take: (only looking at the sin(alpha) part as that neefs to be equal) using trig identity -...

The correct solution uses angles and trigonometry. My solution is as following: - Suppose the forces exerted by friends 1 and 2 are F1 and F2 respectively. - There are no net force in the x-direction, so F(total x) = 0. - F(total y) = F1 + F2 - mg = 0 (initially). Rearranging gives g =...

Find the Mark scheme solution here; Now find my approach; Using the trig. identities It follows that, ##\frac {1}{\sqrt 2}##⋅ ##sin ∅##+##\frac {1}{\sqrt 2}##⋅ ##cos ∅##=##{\sqrt 3}##⋅ ##cos ∅##+##sin ∅## →##sin ∅##[##\frac {1}{\sqrt 2}##-##1]##=##cos ∅##[##\frac {-1}{\sqrt 2}##+##{\sqrt...

I am teaching myself math and wondering if any of you have recommendations on trigonometry books for beginners and self study. Any help is appreciated!

Use the data from the website sunrise-sunset . org / us / lowell-ma to build a model (a sinusoidal function) whose output is the number of hours of daylight in Lowell when the input is the ordinal date (1 though 366) of the year 2020. Find (and show your calculations for finding): Amplitude...

Now i was just doing some random study and i saw this problem on the internet. The problem was to find angle ##B## now there were several responses, let me screen shot one that i think was a bit straightforward... my question is, "is there a much simpler way to find the angle ##B##"?

I was just looking at the problem below: there may be several ways to prove the identity: question: Mark scheme solution: My take: we may also use ##sin^{2}x+cos^{2}x≡(sin x+ cos x)(sin x-cosx)##... we end up with(##\frac 2 {\sqrt{2}}##cos ∅)(##\frac 2...

https://www.upworthy.com/3700-year-old-babylonian-stone-tablet-gets-translated-changes-history

Looking for some guidance on how to set up the equations for a projectile intercept given that you have perfect information about the target velocity, size and weather conditions in a 3D scenario, it's for an amateur videogame that I'm developing in my spare time For simplicity sake let's...

Here is my attempt to draw a diagram for this problem: I'm confused about the "the perpendicular bisector of ##BC## cuts ##BA##, ##CA## produced at ##P, \ Q##" part of the problem. How does perpendicular bisector of ##BC## cut the side ##CA##?

The Figure My Attempt at Solution ##\tan{ACB} = \frac{AB}{BC}, \ \tan41.45^\circ = \frac{AB}{10} \Rightarrow AB = 10\tan45.41^\circ \approx 8.83##cm Similarly ##\tan{CBD} = \frac{CD}{BC}, \ \tan32.73^\circ = \frac{CD}{10} \Rightarrow CD = 10\tan32.73^\circ \approx 6.43##cm After this I...

The sketch: First of all find the length of PQ on i.e $$4 \ inches - 1 \ mile$$ $$1.2 \ inches - x \ mile$$ $$x = \frac{1.2}{4} = 0.3 \ mile = 1584 \ ft$$ Now, I do not understand where shall I draw the horizontal, and the connection between the lengths of the contours, so I'll be grateful if...

Hello, I don't know anything about cricket, so I'll be grateful if you help me with constructing a diagram for this problem. Here's my attempt. I looked up on the internet and I pretty much get the idea of pitches and wickets, but still cannot connect everything together. Thank you.

Suppose the angles in triangle ABC is A, B, and C. If sin A + sin B = 2 sin C, the value of $$2tan\frac12Atan\frac12B$$ is ... A. $$\frac83$$ B. $$\sqrt6$$ C. $$\frac73$$ D. $$\frac23$$ E. $$\frac13\sqrt3$$ Since A, B, and C are the angles of triangle ABC, then C = 180° – (A + B) sin A + sin B...

So what I did first was made the face of the triangle flat and calculated the angle the light entered it. This means the light enters the triangle from the base corner angle (so (180-38.8)/2) of 70.6 degrees. 1sin(70.6)=1.47sin(angle) angle=39.915 Now I need to find the angle it exits. But...

Is it possible to do the integration? That is the full question I don't know where to start, try to use ##u=\cos x## and also ##\cos^2 (x) = \frac{1}{2} + \frac{1}{2} \cos (2x)## but failed. Thanks

Hello! I'm trying to solve this problem. Here's the diagram I tried to make. I have difficulty understanding this math problem.. I've tried to solve the problem using the symmetry of the triangles but I didn't get the right answer, and I can't seem to understand the "concept" of the horizon...

I need only equations on this one

I tried the openstax book Algebra And Trigonometry but i wish there was some better books that teaches trigonometry , anything else i should tried to read ?

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...

What are the units of the trigonometric functions sinus, cosinus etc? If I take say Sin(0.5), what would the units of the output be?

Can you review this high school trigonometry course. I am having a hard time finding a course about trigonometry for intermediates. I am clear with my basics and want to dive in deep now.Thanks for any suggestions!http://www.mecmath.net/trig/trigbook.pdf

Hey, I am new to this community and I am in need of help with this physics problem. I have used the formula above and the answer I get is 1.43s. The correct two answers are 0.68s and 2.4s. For the Vf the answer is 8.3 m/s.

$$\lim_{x\to0}\frac{sin2x+sin6x+sin10x-sin18x}{3sinx-sin3x=}$$ A. 0 B. 45 C. 54 D. 192 E. 212 Either substituting or using L'Hopital gives $$\frac00$$. Is there any way to simplify it and make the result a real number?

1. Using the formula for the arc length; s= θr I have endeavoured to find the angle AOB sine both the arc length and radius are known; 11= θ*8 θ=11/8=1.375 rad I actually do not think that this can be correct as it seem to simplistic a response. Have I misinterpreted the question or used the...

The set of real numbers x at the interval [0, 2π ] which satisfy $$2sin^2x\geq3cos2x+3$$ takes the form [a, b] ∪ [c, d]. The result of a + b + c + d is ... a. 4π b. 5π c. 6π d. 7π e. 8π What I've done thus far: $$2sin^2x\geq3cos2x+3$$ $$2sin^2x\geq3(cos2x+1)$$...

I

kindly note that this solution is NOT my original working. The problem was solved by my colleague. I have doubts with the ##k## value found. Is it not supposed to be ##k=0.5?## as opposed to ##k=2?##. From my reading on scaling, the graph shrinks when ##k## is greater than ##1## and conversely.

Faraday's law: \epsilon=-N\dfrac{\Delta{\phi}}{\Delta{t}}=-N\dfrac{\Delta{(BA\cos{\theta})}}{\Delta{t}}=-N\dfrac{\Delta{(BA\cos{(\omega t)})}}{\Delta{t}} Applying calculus \epsilon=NBA\omega\cos{(\omega t)} Shouldn't it be \epsilon=NBA\omega\sin{(\omega t)}, just if I apply limits? Thanks

##a^2= \frac {sin^4θ} {cos^2θ}## ##b^2=\frac {cos^4θ} {sin^2θ}## therefore ##a^2b^2= sin^2θ. cos^2θ##...1 and ##a^2+b^2+3= \frac {sin^6θ + cos^6θ + 3 sin^2θ cos^2θ} {sin^2θ cos^θ}##...2 multiplying 1 and 2, we get, ##sin^6θ + cos^6θ + 3 sin^2θ cos^2θ## how do i proceed from...

I have tried multiple methods to solve this but have been unsuccessful at every attempt. The apparent correct answer is:

I got answer to (a), which is 3/4 sin thteta - sin ((3^(n+1)) theta) / (4 . 3^n) but I do not know how to use this result to prove next question. I tried to change theta into pi/2 - theta so that sin change to cos or vice versa but not working. Thanks

If $$\alpha+\beta+\gamma=180°$$, prove that $$2sin\alpha+2sin\beta+2sin\gamma=4sin\alpha sin\beta sin\gamma$$! All I knew is that $$sin(\beta+\gamma)=sin(180°-\alpha)=sin\alpha$$, but I think it doesn't help in this case.

Summary: I need to translate points on coordinate axes as part of a calculation process Hello everyone, I've created the diagram below to try and explain what I am trying to do as part of an existing software app that's used to generate profiles and programs to drive a CNC machine to grind...

Speaking of trigonometry without a calculator, I usually only memorizes the trig values of 30°, 45° and 60°. then by I can apply basic equations and applying to polygons or other geometry shapes I can get trig values for angles like 15° Or 75°. When people have enough time, people on Wikipedia...

Homework Statement: (cos2A -1)/sinA +sin2A/(cos2A+1)*cosA=__________________ Homework Equations: sin2A=2sinAcosA cos2A+1=cos^2A cos2A-1=sin^2A (cos2A -1)/sinA +sin2A/(cos2A+1)*cosA [cos^2(2A)-1 +2sin^2(A)cos^2(A)]/sinA(cos2A+1) [-sin^2(2A) + 2sin^2(A)cos^2(A)]/sinA(cos2A+1) I can't proceed...

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...

b^2-1= tan^2(x) + cot^2(x) + 2 -1 b^2-1= sin^2(x)/cos^2(x) +cos^2(x)/sin^2(x) -1 b^2-1=[sin^4(x) +cos^4(x)]/sin^2(x)cos^2(x) -1 b^2-1=[1-sin^2(x)cos^2(x)]/sin^2(x)cos^2(x) -1 a(b^2-1)=sinx+cosx {[1-sin^2(x)cos^2(x)]/sin^2(x)cos^2(x) -1 } I am not able to go any further than this step to reach...

Hi Guys I need help with this question so if you can help me with the answer please please.

I'm building a bed bench and I have an interesting trig problem that I can't figure out. I have a rectangle with known values and a parallelogram that bisects it with a known width. Like a board. I want to be able to figure out the angles so I can cut it. I want the board to intersect the...

Hi all, I found this problem in a new textbook I'm working through. And my energy conservation equation was ## mg\frac {h}{2} = \frac {1}{2} I ω^2 + mg \frac {h}{2}*sin(55) ## My solution was wrong and after checking why I found that they used cos(35) as the angle. The rest was the same. I'm a...

The illustrations on this website are perfect. http://trigonography.com/toc/ I hope it'll help!

I have a simple trigonometry problem. I thought of making this as one of the math challenge problems, but it is almost too easy for that. ## \\ ## It is well known that 6 coins (circles) of equal size can be put around a center coin of the same radius, with the outer coins each touching two...

I have attached a word document demonstrating the working out cos i was too lazy to learn how Latex primer works and writing it like I did above would've been too hard too read. I tried to make it as understandable as possible, presenting fractions as ' a ' instead of ' a / b ' . ------ b

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 three points: A, B and C, which are all on the surface of the same sphere. I need to find the xyz coordinates of C. What I know: - the radius of the sphere - the origin of the sphere - the xyz coordinates of A and B - the arc distance from A to C and from B to C - the angle between AB and...

Show that the maximum range of a projectile launched with Vi from Yi=0 is 45 degrees. (HINT: sin20 = 2sinθcosθ)

Hello! I am a third year kinesiology student who is struggling with her biomechanics assignment. Mind you, I haven’t studied physics or trigonometry in four years since i left high school so I really need some help.

3) Hurricane Michael had horizontal winds of Vout = 69 m/s (155 mph). Pair = 1.29 kg/m3. A building with a flat, horizontal roof, Aroof = 200 m2, and Vin = 0 m/s. a) What is the pressure difference, Pin - Pout on the roof. Assume Yin = Yout. b) What is the force acting on the roof, and what...