Cosine Even Property Verification and the use of it to show Cos (x-90) = Cos (90-x)?

Question

Okay, I know that the cosine function is an even function, meaning Cos (x) = Cos (-x)

Therefore Cos (x-90) = Cos (-(x-90)) = Cos (90-x)

My Book writes: As the cosine is an even function, cos (90-x) = cos (x-90).
After plotting the graph using a graph plotter off an Google app,
The graph of cos (x-90) is that of an odd function (symmetry about the origin). So how does that even property of cosine function help show cos (90-x) = cos (x-90)
I mean I know it makes sense that cos (-A) = cos A where A = (x-90).... but when I plot the graph of cos (x-90), it becomes an odd function. So what are the implications here? PLEASE HELP

Answer 1

The fact that cos(x-90) is odd is irrelevant.



Because cosine is an even function:

cos(x-90) = cos( -(x-90) ) = cos(90-x)



You can plug in any other number instead of 90, and it works out the same way.



Suppose we choose 30 degrees instead of 90 degrees:

cos(x-30) = cos( -(x-30) ) = cos(30-x)

cos(30-x) is neither odd nor even, but that doesn't matter, because all that matters here is that cosine is an even function.

Answer 2

Draw a correct perspective triangle. The sum of the angles- like all triangle- is 100 and eighty ranges. Angles A,B,C A is ninety ranges. So B+C = ninety ranges. So B = ninety-C. remember the elementary definition of sin and cos -opposite/hypoteneuse and adjoining/hypoteneuse respectively. Calculate the sine of B and the cosine of C. (undemanding with a sheet of paper and a pencil. more desirable sturdy to describe in words!)

Answer 3

look : cos(-x) = cosx , it's a rule

so : cos(x-90) = cos(-(90-x)) = cos(90-x)

welcome

Answer 4

BELIEVE AYM H HE'S A GENIUS.



But in all seriousness, your calculator is wrong, or you're interpreting it wrong.