In both radians and degrees cos(0) = 1.
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Cosine of -90 is 0.
Reciprocal of Cosine is Secant
it would be secant, 1/cosine
No, not necessarily. Cosine theta is equal to 1 only when theta is equal to zero and multiples of 2 pi radians or multiples of 360 degrees. This is because cosine theta is hypotenuse over adjacent, and the ratio 1 only occurs at 0, 360, 720, etc. or 0, 2 pi, 4 pi, etc.
[ cos(Θ) ]-1 = 1/cosine(Θ) = secant(Θ)