Can cos^2(kt)+sin^2(kt) always equal 1, regardless of the value of k?

[mill]

Where k is a constant.

I am trying to simplify a problem but the t has constant in front of it that is not one, and I can't seem to find a chart that verifies it either way.

 

[slider142]

Yes. cos²θ + sin²θ = 1 for any value of θ, including θ = kt. This is called the Pythagorean identity, and is the result of applying the Pythagorean theorem to the fact that cosθ and sinθ are the x and y coordinates, respectively, of a point on the unit circle (a circle of radius 1).

 

[mill]

Thanks!

 

[MartinSTuray]

Thanks!

Yes. cos²θ + sin²θ = 1 for any value of θ, including θ = kt. This is called the Pythagorean identity, and is the result of applying the Pythagorean theorem to the fact that cosθ and sinθ are the x and y coordinates, respectively, of a point on the unit circle (a circle of radius 1).

...is a brilliant answer to my problem of how to describe force vectors for alloys. Big thanks, slider142. and mill.

 

[MartinSTuray]

Just got back from seaside and found answer to a month's headache. Complementary! B)