I find it conceptually cool, but I struggled in school with learning the identities, memorization being one of my weak areas.

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Sohcahtoa82 3 days ago | parent [-]

If you know your trig well enough, you can derive the identities.

For example, knowing that cosine and sine are the exact same wave, just 90 degrees out of phase, it's trivial to know that sin(angle) = cos(angle + 90)

cos(a)^2 + sin(a)^2 = 1 is easy to show, too. If you use a=0, it's trivial. But try using 45 degrees. It turns into (sqrt(2)/2)^2 + (sqrt(2)/2)^2 which simplifies to 0.5 + 0.5 = 1.

Many of the others can be derived by just manipulating the Law of Sines or Law of Cosines. Fun fact: The Pythagorean Theorem is actually just a special case of the Law of Cosines:

c^2 = a^2 + b^2 - 2*a*b*cos(C)

Recall that in the Law of Cosines as I've written it, the lowercase letters are the sides, and the large C is the angle opposite that side. So if you choose your hypotenuse to be c, then the opposite angle, C, is 90 degrees. cos(90) is 0, so that whole last term gets cancelled out and you're left with the equation known as the Pythagorean Theorem.

I really wasn't kidding when I said I enjoyed trig.

	▲	Sohcahtoa82 3 days ago \| parent [-]
		Too late to edit now, but wanted to add a note: Knowing that cos(45) == sqrt(2)/2 seems like something you would need to memorize, but if you just draw an isosceles right triangle with sides equal to 1 and use the Pythagorean Theorem you'll find that the hypotenuse is sqrt(2)/2.