Trigonometry identity Definition and 13 Threads

Hi, The orthogonality defect is ##\prod_i ||b_i|| / det(B)##. Now it is said: The relation between this quantity and almost orthogonal bases is easily explained. Let ##\theta_i## be the angle between ##b_i## and ##span(b_1,...,b_{i-1})##. Then ##||b_i^*|| = ||b_i|| cos(\theta_i)##. [...] So...

Refreshing on trig. today...a good day it is...ok find the text problem here; With maths i realize one has to keep on refreshing at all times... my target is to solve 5 questions from a collection of 10 textbooks i.e 50 questions on a day-day basis...motivation from late Erdos...

Can someone please tell me how sin(180 - x) = sin x? Here my attempt: sin (180 - x) = sin 180 . cos x - cos 180 . sin x Next? I have no idea...

For the given triangle as below: I can obtain trigonometry identities as below: ##\sin α = \frac{y}{r} = \cos (90° - α)## ##\cos α = \frac{x}{r} = \sin (90° - α)## ##\tan α = \frac{y}{x} = \cot (90° - α)## ##\cot α = \frac{x}{y} = \tan (90° - α)## ##\sec α = \frac{r}{x} = \csc (90° - α)##...

Homework Statement Use the substitution ##u=\frac{\pi} {2}-x## evaluate the integral ##\int_0^\frac {\pi}{2} \frac {\sin x}{\cos x + \sin x}dx##. Homework Equations [/B] ##\cos (\frac {\pi}{2}-x)=\sin x## The Attempt at a Solution [/B]I start by plugging "u" into the equation making the...

1) Question: Show that (sin3A-sinA)/(cosA+cos3A)=tanA 2) Relevant equations: tan A=sinA/cos A 1+tan^2A=sec^A cot A=1/tanA cot A=cos A/sinA sin^2A+cos^2A=1 secA=1/cos A cosecA=1/sinA 1+cosec^2A= cot^2A sin2A=2sinAcosA cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1 tan2A=(2tanA)/1-tan^2A 3)Attempt...

Homework Statement The problem is f(x) = sin2πx - (1/πsquare)*sinπx and its given Bn sin (nπx) = f(x) Question is find Bn. Homework Equations Bn = 2/L ∫ (sin2πx - (1/πsquare)*sinπx) * sin(nπx/L) where L is 1 The Attempt at a Solution I did [/B] ∫ sin2πx * sin (nπx) - (1/πsquare)*sin...

Homework Statement I understand the setup for finding the slope, but always get confused whether I've fully simplified when trig identities get involved. [/B] Homework Equations My dy/dx is [/B] 4sin(θ)cos(θ) -2csc2(θ) which I simplified to just (-2sin(θ)cos(θ))/(csc2(θ) Does that...

Homework Statement Hi guys, How can sin(∏)cos(ω∏)-cos(∏)sin(ω∏) = sin(ω∏)? please guide me trigonometry identity to apply with this? Homework Equations The Attempt at a Solution

I'm working on some trigonometry identity problems, and I'm stuck on this particular problem. This is how it is shown in the solution, but I cannot see how to get the highlighted part. Any help on how to get from #2 to #3 (the highlighted) is very much appreciated Jesper

Homework Statement solve 3cos(x) + 3 = 2 sin^2(x) where 0 <= x < 2piHomework Equations The Attempt at a Solution 3(cos(x) + 1) = 2 sin^2(x) 3(cos(x) + 1) = 2 (1- cos^2(x)) I've tried this variation, and a couple others but it just does not pan out. Please help. Oh yeah we have a real...

Someone pls help me prove this identity. I'm going nuts :confused: tan^2x - sin^2x = tan^2x sin^2x

I can do pretty much all the proofs except these two, though I've tried to make a start. Note that in the questions the angle is given as theta, but for the sake of my keyboard I've changed it to angle 'x'. Q15: Prove: Tan2xsecx = 2sinxsec2x. So I need to show the two sides are equal...