I don't know how to prove sin^2(x)+cos^2(x)=1
89 views (last 30 days)
Show older comments
I want to prove this thing by Matlab
sin^2 (x) + cos^2 (x) = 1
Somebody help me.
Please.....
1 Comment
Accepted Answer
More Answers (3)
Ameer Hamza
on 17 Nov 2020
Edited: Ameer Hamza
on 17 Nov 2020
If you have symbolic toolbox, you can use isAlways()
syms x
eq = sin(x)^2 + cos(x)^2 == 1;
tf = isAlways(eq)
value of 1 means that it is correct for all values of 'x'.
0 Comments
James Tursa
on 17 Nov 2020
Edited: James Tursa
on 17 Nov 2020
[cos(x),sin(x)] is defined to be a point on the unit circle, so by definition we have sin^2(x) + cos^2(x) = 1 always. This isn't something to be proved since it is a definition. If you want to demonstrate it with values, you can always just plug stuff in and see that you always get about 1 within numerical floating point errors, or make x symbolic and evaluate the expression. But, this will just be a "feel good" demonstration ... it doesn't prove anything since the result follows directly from the definition.
0 Comments
Bruno Luong
on 17 Nov 2020
Edited: Bruno Luong
on 17 Nov 2020
Definition
exp(x) = sum x^k/factorial(k).
exp(x+y) = exp(x)*exp(y)
Definitions
sin(x) = 1/(2i) (exp(ix) - exp(-ix))
cos(x) = 1/2 (exp(ix) + exp(-ix))
Thus using exp(0) = 1, i^2=-1
sin(x)^2 = -1/4 (exp(2ix) + exp(-2ix) -2)
cos(x)^2 = +1/4 (exp(2ix) + exp(-2ix) +2)
When sum it all the exp terms go away and we get
sin(x)^2 + cos(x)^2 = 1
(then one can deduce (sin(x),cos(x)) is point on circle, NOT the opposite definition of sin(x) is abcissa coordinate of point on circle bla bla bla).
0 Comments
See Also
Categories
Find more on Resizing and Reshaping Matrices in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!