Recent content by jayanthd

Applying limits on the last step was not a problem. I was getting wrong answer that is there was a mistake in sign at one place where Integration by parts is done second time. After fixing it I got the right answer which I have modified in post 1. After applying the limits I got the right...

Homework Statement Why I am getting wrong answer related to this Laplace Transforms problem? According to the book "Higher Engineering Mathematics 6th edition by John O Bird" page no. 583 one should get (e^{-st}/(s^{2} + a^{2}))(a sin at - s cos at)Homework Equations ∫e^{-st}cos at dt The...

Thank you CompuChip and SteamKing. CompuChip my question was I know I have to apply limits to the two (e−10τ / - 10) I want to know should I apply limits also to τ which is at the beginning of the solution (here... = 200 [ τ ...) ? Yes, CompuChip the solution you gave is what I have. I was...

I know ∫(xe^{ax}) dx = x (e^{ax} / a) - (1/a) ∫e^{ax} . 1 dx = x (e^{ax} / a) - (1/a) (e^{ax} / a) = (e^{ax} / a) (x - 1/a) i.e, integral of two functions = (first function) (integral of second function) - ∫(integral of second function) (differential of first function) This is not a...

He is proving with the top four figures that sin(90 - θ ) = cos(θ). It is from the book "Theory and Problems of Plane and Spherical Trigonometry by Frank Ayres, Schaum's Outline Series" The book is available here. http://archive.org/details/SchaumsTheoryProblemsOfTrigonometry Please...

Please see the attached image. There are 6 figures. Please explain the proofs for sin(90 - θ) w.r.t the 2nd, 3rd and 4th images. I understand the proof w.r.t 1st image. In the 2nd image y1 and x is negative. In 3rd image y, y1, x, x1 are all negative and in the 4th image y and x1 are...

Thank you very much. I had not seen that the slope dy/dx of the equation was given as 9.

I have a small problem in solving a Second Order Linear Constant Coefficient Differential Equation. Please see the attached image. I understand upto the point above the arrow. What I don't understand is how he got dy/dx = 9

Thank you very much. Now it is clear to me. I have similar problem with sin(180 - θ). Edit: Now another question is regarding 180 - θ. See images. Now tell me how sin(AOP') = sin θ. Is this right? sin(180 - θ) = sin(180 - (180 - θ)) = sin(θ) ??

Trigonometry Proofs Here are the images. Consider the 2nd image for the drawing.

I know that a right angled triangle can have angles 90, θ, and (90 - θ) but how did S L Loney proves sin(90 + θ) = cos(θ) as mentioned in the first post. Is it that nobody here knows geometrical proof for sin(90 + θ) and sin(180 - θ)?

Because I can't memorize sin(90 + theta), sin(90 - theta), sin(180 - theta), sin(180 + theta) and other ratios. If explained geometrically then it will be easy to derive whenever needed. I know the Unit Circle approach.

I know that solution. What I need is geometrical proof using right angled triangle.

I have seen that link. It doesn't tell how sin(90 - θ) becomes sin(90 + θ). Can you please explain. This is the only thing in Trigonometry that I am not able to understand.

Can you explain in detail. Please explain how the author considers sin(90 - θ) as sin(90 + θ).