Where does the pythagorean identity sin2 θ + cos2 θ = 1 come from? how would you use it to find the sine cosine and tangent values of the angle?

Imagine a trigonometric circle with radius equal to 1.

We can say that the opposite side of the angle generated by the origin is equal to sen Ф and the adjacent equal to cos Ф

With this we can say that:

h² = c² + c²

If r = 1, then h = 1

1² = cos² + sen²

1 = cos² Ф + sen² Ф

You can use this equation a lot of times because it's the fundamental trigonometric relation
, so, when you something like:

sen Ф = cos Ф + 1

you can take from sen² Ф + cos² Ф = 1 that and then resolve.

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step-by-step explanation: