why is sin(90-θ) = cosθ?
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There are many explanations. This is the dumbest one:
In a right triangle, the sine is defined as the opposite side divided by the hypothenuse. The cosine is the adjactent side divided by the hypothenuse.
If you take either angle and substract it from 90, you’ve basically calculated the remaining angle of the triangle (other than the right angle itself). That’s because the sum of angles in any triangle is 180°, so finding the unknown angle is equivalent to solving 180=x+90+θ for x. That yields x=90-θ.
However, from x’s perspective, the opposite side (to θ) is the adjacent side. And vice versa. So the cosine of x is just the sine of θ. And vice versa. That’s why sin(90-θ) is just the cos(θ).
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