trigonometric identity Definition and Topics - 7 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.
(Sinx-2cosx)/ (cotx - sinx)
Substitute tan instead of cot
(Tanx(sinx-2cosx)/(1-sinx)
What do I do from here
I don't think what I did there is correct
That's why I didn't expand the tan to sin/cos
I'm trying to make an approximation to a series I'm generating; the series is constructed as follows:
Term 1:
\left[\frac{cos(x/2)}{cos(y/2)}\right]
Term 2:
\left[\frac{cos(x/2)}{cos(y/2)}-\frac{sin(x/2)}{sin(y/2)}\right]
I'm not sure yet if the series repeats itself or forms a pattern...
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...
Hi,
This is also a sort of geometry question.
My textbook gives a proof of the relation: sin(θ + Φ) = cosθsinΦ + sinθcosΦ.
It uses a diagram to do so:
http://imgur.com/gLnE2Fn
sin (θ + Φ) = PQ/(OP)
= (PT + RS)/(OP)
= PT/(OP) + RS/(OP)
= PT/(PR) * PR/(OP) + RS/(OR) * OR/(OP)
= cosθsinΦ +...
Homework Statement
Prove the following trigonometric identity. The question is sin^4Ө =3/8-3/8cos(2Ө)
Homework Equations
I think I'm supposed to use the power reducing formulas for trigonometric identities which are
sin^2(u)= (1- cos(2u))/2
cos^2(u)=(1+cos(2u))/2
*Let u represent any...
EDIT: I figured out my mistake...no option to delete silly post. Oh well.
1. Homework Statement
The problem is: use iterated integrals in polar form to find the area of one leaf of the rose-shaped curve r = cos(3*theta).
My setup agrees exactly with the solutions manual...but then something...