Question

Will give medal to best answer! The expression cos^-1 (3/5) has an infinite number of values.
True or False??
I think it's false.

Answer 1

@divu.mkr

Answer 2

false

Answer 3

\[\cos ^{-1}\frac{ 3 }{ 5 }\] has a solution in the first quadrant and another in the fourth quadrant, and that's just on the interval\[\left[ 0,2\pi\right]\]

Answer 4

but it happens that the cosine function is periodic; therefore, its graph repeats itself every 2pi radians.

Therefore, \[\cos ^{-1}\frac{ 3 }{ 5 }\] is far from being the only solution.

Answer 5

Starting with the solution (angle) that's in the first quadrant, this inverse function has infinitely many solutions:

\[\theta(plus.or.minus) n2\pi,\], for n={0,1,2,3,4,..... }

Answer 6

and a similar expression can be written for the solution whose initial value is in Q4.

Answer 7

So: What is your answer to the original question?

Answer 8

well it was false at first..

Answer 9

but now I'm thinking it's true?

Answer 10

And now your answer is:

Answer 11

true?

Answer 12

no, it's false. Cosine inverse a one-to-one function.

Answer 13

@ranga