If \sin x^\circ=\cos y^\circ, 0<x<y<90, and xy=800, what is the value of x^2+y^2 ?



Comments (4)

I thought that it meant x^0 or Y^0 which is one(cant be) then I figured it meant angle but this got confusing when it means that its the sin angle associated with x which is the y value divided by the hypotenuse which is equal to the cos value associated with y which is the y value divided by the hypotenuse or the same reference lines associated with the two different trig functions which are complimentary in angle generation

If i’m being honest, I just saw that the inequality given, 0 < x < y < 90, meant that x < y. What I remembered what the complimentary rule, which is sin (x) = cos (90 – x) or vice versa. This helped me remember (similar to what the explanation said) that the angles must add up to 90° (hence why the rule is called the “complimentary” rule :)).

So, at this point I just found 2 numbers that multiply to 800 and add to 90, which is 80 and 10. 80^2 + 10^ 2 = 6500.

Answer = 6500

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