the law of cosines bears strong similarities to the pythagorean theorem. according to the law of cosine if two sides of a triangle have lengths a and b and if the angle between them has a measurement of x then the length of y of the third side of the triangle can be found by using the equation y^2=a^2=b^2-2ab cos(x degree)

if the value of x becomes less and less, what number is cos(x degree) close to?

Question

the law of cosines bears strong similarities to the pythagorean theorem. according to the law of cosine if two sides of a triangle have lengths a and b and if the angle between them has a measurement of x then the length of y of the third side of the triangle can be found by using the equation y^2=a^2=b^2-2ab cos(x degree)

if the value of x becomes less and less, what number is cos(x degree) close to?

anonymous · Answer

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zzr0ck3r · Answer

law of cosines is a more general version of Pythagorean theorem

phi · Answer

if the value of x becomes less and less, what number is cos(x degree) close to?

in other words, what is cos(0) ?

anonymous · Answer

yea but the question is if the value of x becomes less and less, what number is cos(x degree) close to? @zzr0ck3r

zzr0ck3r · Answer

this is a weird question, it seems that if they wanted to make the point of Pythagorean theorem related to law of cosines they would ask what happens as we get close to 90 degrees

zzr0ck3r · Answer

phi is right

anonymous · Answer

1 ?? @phi

zzr0ck3r · Answer

$$\lim_{x\rightarrow 0}\cos(x)=1$$ this is the notation one might use

phi · Answer

yes, 1.

when angle x is 0º, the line labeled a lines on top of the horizontal line b

anonymous · Answer

thanks guy!! it was right @phi @zzr0ck3r

phi · Answer

your equation
y^2=a^2+b^2-2ab cos(x degree)
turns into
y^2 = a^2 -2ab + b^2
which (you may know) is the same as
y^2 = (a-b)^2

and y= difference between a and b