What is Trigonometry identity: Definition and 13 Discussions
In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle.
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
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...
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...
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...
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...