why is sin(90-θ) = cosθ?
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Sin and cos are the y and x values, respectively, of a point on the unit circle. Because you can drop a vertical line from any point on the unit circle and form a right triangle, and because the formula of the unit circle is x^2 + y^2 = 1, you can also find another right triangle on the circle by flipping the x and y coordinates. But the two angles opposite the distances x and y are complementary (because the third angle of the triangle is always a right angle by the definition of how we are constructing the triangle), so the sin of one of them must be the cos of the other and vice versa.
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