sin(x) and cos(x) return the side lengths of a triangle with hypotenuse 1 and angle x, like so:
I also was never taught this, which sucks because it’s such a useful concept.
You can verify that if the angle (x) was 0, cos(x) would be 1, and sin(x) would be 0. If the angle was 90 degrees (vertical), then cos(x) would be 0 and sin(x) would be 1. If the angle was 45 degrees, cos(x) and sin(x) would have the same value, because the triangle sides would have the same length.
See, I was taught this, but no one could every answer why sine and cosine worked the way they did.
This definition just explains how they work with triangles. What’s the actual definition of each, and how was that derived? I can apply them all day long yet I still can’t tell you what either one means.
I had the same issues with different kinds of equations, no one ever explained why you’d do a certain thing in a given step (e.g. Quadratic) even when I asked, repeatedly. The answer was always “you just do”. Well that doesn’t help with knowing when to apply a rule.
And that was my experience with any math, right through college (3 universities). Most teachers suck, but holy shit math teachers are down right moronic. They can’t understand why students don’t get it. Well, try actually teaching something for a fucking change.
sin(x) and cos(x) return the side lengths of a triangle with hypotenuse 1 and angle x, like so:
I also was never taught this, which sucks because it’s such a useful concept.
You can verify that if the angle (x) was 0, cos(x) would be 1, and sin(x) would be 0. If the angle was 90 degrees (vertical), then cos(x) would be 0 and sin(x) would be 1. If the angle was 45 degrees, cos(x) and sin(x) would have the same value, because the triangle sides would have the same length.
But why?
See, I was taught this, but no one could every answer why sine and cosine worked the way they did.
This definition just explains how they work with triangles. What’s the actual definition of each, and how was that derived? I can apply them all day long yet I still can’t tell you what either one means.
I had the same issues with different kinds of equations, no one ever explained why you’d do a certain thing in a given step (e.g. Quadratic) even when I asked, repeatedly. The answer was always “you just do”. Well that doesn’t help with knowing when to apply a rule.
And that was my experience with any math, right through college (3 universities). Most teachers suck, but holy shit math teachers are down right moronic. They can’t understand why students don’t get it. Well, try actually teaching something for a fucking change.
Look up a diagram of a cosine and sine functions as they relate to a rotating circle.
E.g.: https://upload.wikimedia.org/wikipedia/commons/3/3b/Circle_cos_sin.gif